Top Read Articles

    Published in last 1 year |  In last 2 years |  In last 3 years |  All
    Please wait a minute...
    BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS
    Boyong Chen, Liangying Jiang
    Acta mathematica scientia,Series B    2024, 44 (3): 789-809.   DOI: 10.1007/s10473-024-0301-1
    Abstract185)            Save
    In this article, we investigate the (big) Hankel operator $H_f$ on the Hardy spaces of bounded strongly pseudoconvex domains $\Omega$ in $\mathbb{C}^n$. We observe that $H_f$ is bounded on $H^p(\Omega)$ ($1< p<\infty$) if $f$ belongs to BMO and we obtain some characterizations for $H_f$ on $H^2(\Omega)$ of other pseudoconvex domains. In these arguments, Amar's $L^p$-estimations and Berndtsson's $L^2$-estimations for solutions of the $\bar{\partial}_b$-equation play a crucial role. In addition, we solve Gleason's problem for Hardy spaces $H^p(\Omega)$ ($1\le p\le\infty$) of bounded strongly pseudoconvex domains.
    Reference | Related Articles | Metrics
    LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY*
    Zhongmin Qian, Xingcheng Xu
    Acta mathematica scientia,Series B    2024, 44 (5): 1609-1638.   DOI: 10.1007/s10473-024-0501-8
    Abstract143)            Save
    This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering.
    Reference | Related Articles | Metrics
    THE GRADIENT ESTIMATE OF SUBELLIPTIC HARMONIC MAPS WITH A POTENTIAL
    Han Luo
    Acta mathematica scientia,Series B    2024, 44 (4): 1189-1199.   DOI: 10.1007/s10473-024-0401-y
    Abstract134)            Save
    In this paper, we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations. Under some suitable conditions, we give the gradient estimates of these maps and establish a Liouville type result.
    Reference | Related Articles | Metrics
    MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS
    Quanquan Yao, Peiyong Zhu
    Acta mathematica scientia,Series B    2024, 44 (4): 1200-1228.   DOI: 10.1007/s10473-024-0402-x
    Abstract102)            Save
    Let $(X,T)$ be a linear dynamical system, where $X$ is a Banach space and $T:X \to X$ is a bounded linear operator. This paper obtains that $(X,T)$ is sensitive (Li-Yorke sensitive, mean sensitive, syndetically mean sensitive, respectively) if and only if $(X,T)$ is Banach mean sensitive (Banach mean Li-Yorke sensitive, thickly multi-mean sensitive, thickly syndetically mean sensitive, respectively). Several examples are provided to distinguish between different notions of mean sensitivity, syndetic mean sensitivity and mean Li-Yorke sensitivity.
    Reference | Related Articles | Metrics
    SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENTS OF FOCK-SOBOLEV SPACES
    Yong CHEN, Young Joo LEE
    Acta mathematica scientia,Series B    2024, 44 (3): 810-822.   DOI: 10.1007/s10473-024-0302-0
    Abstract99)            Save
    We consider dual Toeplitz operators on the orthogonal complements of the ock-Sobolev spaces of all nonnegative real orders. First, for symbols in a certain class containing all bounded functions, we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero. Next, for bounded symbols, we construct a symbol map and exhibit a short exact sequence associated with the $C^*$-algebra generated by all dual Toeplitz operators with bounded symbols.
    Reference | Related Articles | Metrics
    STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION
    Mohsan Raza, Hadiqa Zahid, Jinlin Liu
    Acta mathematica scientia,Series B    2024, 44 (4): 1244-1270.   DOI: 10.1007/s10473-024-0404-8
    Abstract98)            Save
    Let $q_{\lambda }\left( z\right) =1+\lambda \sinh (\zeta ),\ 0<\lambda <1/\sinh \left( 1\right) $ be a non-vanishing analytic function in the open unit disk. We introduce a subclass $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ of starlike functions which contains the functions $\mathfrak{f}$ such that $z\mathfrak{f}^{\prime }/\mathfrak{f}$ is subordinated by $q_{\lambda }$. We establish inclusion and radii results for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $ for several known classes of starlike functions. Furthermore, we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class $\mathcal{S}^{\ast }\left( q_{\lambda }\right) $. We also find a sharp bound for the third Hankel determinant for the case $\lambda =1/2$.
    Reference | Related Articles | Metrics
    ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA*
    Zhanjie SONG, Jiaxing ZHANG
    Acta mathematica scientia,Series B    2024, 44 (5): 1984-1996.   DOI: 10.1007/s10473-024-0521-4
    Abstract95)            Save
    In this paper, we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field. By estimating the probability value of a time-stationary random field in a small range, we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region. It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1. In addition, we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.
    Reference | Related Articles | Metrics
    APPROXIMATION PROBLEMS ON THE SMOOTHNESS CLASSES*
    Yongping LIU, Man LU
    Acta mathematica scientia,Series B    2024, 44 (5): 1721-1734.   DOI: 10.1007/s10473-024-0505-4
    Abstract92)            Save
    This paper investigates the relative Kolmogorov $n$-widths of $2\pi$-periodic smooth classes in $\widetilde{L}_{q}$. We estimate the relative widths of $\widetilde{W}^{r} H_{p}^{\omega}$ and its generalized class $K_{p}H^{\omega}(P_{r})$, where $K_{p}H^{\omega}(P_{r})$ is defined by a self-conjugate differential operator $P_{r}(D)$ induced by $P_{r}(t):= t^{\sigma} \Pi_{j=1}^{l}(t^{2}- t_{j}^{2}),~t_{j} > 0,~j=1, 2 ,\cdots, l,~l \geq 1,~\sigma \geq 1,~r=2l+\sigma .$ Also, the modulus of continuity of the $r$-th derivative, or $r$-th self-conjugate differential, does not exceed a given modulus of continuity $\omega$. Then we obtain the asymptotic results, especially for the case $p=\infty , 1\leq q \leq \infty$.
    Reference | Related Articles | Metrics
    HEAT KERNEL ON RICCI SHRINKERS (II)*
    Yu Li, Bing Wang
    Acta mathematica scientia,Series B    2024, 44 (5): 1639-1695.   DOI: 10.1007/s10473-024-0502-7
    Abstract85)            Save
    This paper is the sequel to our study of heat kernel on Ricci shrinkers [29]. In this paper, we improve many estimates in [29] and extend the recent progress of Bamler [2]. In particular, we drop the compactness and curvature boundedness assumptions and show that the theory of $\mathbb{F}$-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.
    Reference | Related Articles | Metrics
    THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE
    Saiguo Xu, Zhong Tan
    Acta mathematica scientia,Series B    2024, 44 (4): 1466-1486.   DOI: 10.1007/s10473-024-0415-5
    Abstract84)            Save
    This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena. The Boussinesq system focused on here is anisotropic, and involves only horizontal dissipation and thermal damping. In the 2D case $\mathbb{R}^2$, due to the lack of vertical dissipation, the stability and large-time behavior problems have remained open in a Sobolev setting. For the spatial domain $\mathbb{T}\times\mathbb{R}$, this paper solves the stability problem and gives the precise large-time behavior of the perturbation. By decomposing the velocity $u$ and temperature $\theta$ into the horizontal average $(\bar{u},\bar{\theta})$ and the corresponding oscillation $(\tilde{u},\tilde{\theta})$, we can derive the global stability in $H^2$ and the exponential decay of $(\tilde{u},\tilde{\theta})$ to zero in $H^1$. Moreover, we also obtain that $(\bar{u}_2,\bar{\theta})$ decays exponentially to zero in $H^1$, and that $\bar{u}_1$ decays exponentially to $\bar{u}_1(\infty)$ in $H^1$ as well; this reflects a strongly stratified phenomenon of buoyancy-driven fluids. In addition, we establish the global stability in $H^3$ for the 3D case $\mathbb{R}^3$.
    Reference | Related Articles | Metrics
    THE $\rm BSE$ PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS*
    Fatemeh Abtahi, Ali Rejali, Farshad Sayaf
    Acta mathematica scientia,Series B    2024, 44 (5): 1945-1954.   DOI: 10.1007/s10473-024-0518-z
    Abstract83)            Save
    In this paper, $X$ is a locally compact Hausdorff space and ${\mathcal A}$ is a Banach algebra. First, we study some basic features of $C_0(X,\mathcal A)$ related to $\rm BSE$ concept, which are gotten from ${\mathcal A}$. In particular, we prove that if $C_0(X,\mathcal A)$ has the $\rm BSE$ property then $\mathcal A$ has so. We also establish the converse of this result, whenever $X$ is discrete and $\mathcal A$ has the BSE-norm property. Furthermore, we prove the same result for the $\rm BSE$ property of type I. Finally, we prove that $C_0(X,{\mathcal A})$ has the BSE-norm property if and only if $\mathcal A$ has so.
    Reference | Related Articles | Metrics
    THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS*
    Yifang yang, Jinping wang
    Acta mathematica scientia,Series B    2024, 44 (5): 1787-1800.   DOI: 10.1007/s10473-024-0509-0
    Abstract81)            Save
    In this paper, we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit (BgOMP) algorithm in the $l_2$-bounded noise case. Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal, if the sensing matrix satisfies the the block restricted isometry property (block-RIP), then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations. Furthermore, we conjecture that this condition is sharp.
    Reference | Related Articles | Metrics
    ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE $p$-LAPLACIAN DIFFUSION
    Rui Huang, Yong Wang, Zhuo Yin
    Acta mathematica scientia,Series B    2024, 44 (4): 1550-1571.   DOI: 10.1007/s10473-024-0420-8
    Abstract78)            Save
    We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate $p$-Laplacian diffusion. We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods. Moreover, we show the existence and regularity of an original solution via a compactness analysis. Finally, we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.
    Reference | Related Articles | Metrics
    VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES*
    Ziyi Zhou, Yi Jiang
    Acta mathematica scientia,Series B    2024, 44 (5): 1696-1706.   DOI: 10.1007/s10473-024-0503-6
    Abstract75)            Save
    For a general normed vector space, a special optimal value function called a maximal time function is considered. This covers the farthest distance function as a special case, and has a close relationship with the smallest enclosing ball problem. Some properties of the maximal time function are proven, including the convexity, the lower semicontinuity, and the exact characterizations of its subdifferential formulas.
    Reference | Related Articles | Metrics
    MULTIPLE SOLUTIONS TO CRITICAL MAGNETIC SCHRÖDINGER EQUATIONS
    Ruijiang Wen, Jianfu Yang
    Acta mathematica scientia,Series B    2024, 44 (4): 1373-1393.   DOI: 10.1007/s10473-024-0411-9
    Abstract73)            Save

    In this paper, we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation

    $\begin{matrix}(-{\rm i}\nabla-A(x))^2u+\lambda V(x)u=\mu |u|^{p-2}u+\Big(\int_{\mathbb{R^N}}\frac{|u(y)|^{2^*_\alpha}}{|x-y|^\alpha}{\rm d}y\Big)|u|^{2^*_\alpha-2}u\quad {\rm in}\ \mathbb{R}^N,\end{matrix}$ (0.1)

    where $N\geq4$, $2\leq p<2^*$, $2^*_\alpha=\frac{2N-\alpha}{N-2}$ with $0<\alpha<4$, $\lambda>0$, $\mu\in\mathbb{R}$, $A(x)= (A_1(x), A_2(x),\cdots , A_N(x))$ is a real local Hölder continuous vector function, $i$ is the imaginary unit, and $V(x)$ is a real valued potential function on $\mathbb{R}^N$.Supposing that $\Omega={\rm int}\,V^{-1}(0)\subset\mathbb{R}^N$ is bounded, we show that problem (0.1) possesses at least cat$_\Omega(\Omega)$ nontrivial solutions if $\lambda$ is large.

    Reference | Related Articles | Metrics
    ON A UNIVERSAL INEQUALITY FOR APPROXIMATE PHASE ISOMETRIES
    Duanxu Dai, Haixin Que, Longfa Sun, Bentuo Zheng
    Acta mathematica scientia,Series B    2024, 44 (3): 823-838.   DOI: 10.1007/s10473-024-0303-z
    Abstract73)            Save
    Let $X$ and $Y$ be two normed spaces. Let $\mathcal{U}$ be a non-principal ultrafilter on $\mathbb{N}$. Let $g: X\rightarrow Y$ be a standard $\varepsilon$-phase isometry for some $\varepsilon\geq 0$, i.e., $g(0)=0$, and for all $u,v\in X$,
    $$|\; |\|g(u)+g(v)\|\pm \|g(u)-g(v)\||-|\|u+v\|\pm\|u-v\||\;|\leq\varepsilon.$$
    The mapping $g$ is said to be a phase isometry provided that $\varepsilon=0$.
    In this paper, we show the following universal inequality of $g$: for each $u^*\in w^*$-exp $\|u^*\|B_{X^*}$, there exist a phase function $\sigma_{u^*}: X\rightarrow \{-1,1\}$ and $\varphi$ $\in$ $Y^*$ with $\|\varphi\|= \|u^*\|\equiv \alpha $ satisfying that
    $$\;\;\;\;\; |\langle u^*,u\rangle-\sigma_{u^*} (u)\langle \varphi, g(u)\rangle |\leq\frac{5}{2}\varepsilon\alpha ,\;\;{\rm for\;all\;}u\in X.$$ In particular, let $X$ be a smooth Banach space. Then we show the following:
    (1) the universal inequality holds for all $u^*\in X^*$;
    (2) the constant $\frac{5}{2}$ can be reduced to $\frac{3}{2}$ provided that $Y^\ast$ is strictly convex;
    (3) the existence of such a $g$ implies the existence of a phase isometry $\Theta:X\rightarrow Y$ such that $\Theta(u)=\lim\limits_{n,\mathcal{U}}\frac{g(nu)}{n}$ provided that $Y^{**}$ has the $w^*$-Kadec-Klee property (for example, $Y$ is both reflexive and locally uniformly convex).
    Reference | Related Articles | Metrics
    ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW
    Zhong Tan, Xinliang Li, Hui Yang
    Acta mathematica scientia,Series B    2024, 44 (3): 851-864.   DOI: 10.1007/s10473-024-0305-x
    Abstract72)            Save
    In this paper, we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.
    Reference | Related Articles | Metrics
    GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH $p$-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE
    Xiaoshan Wang, Zhongqian Wang, Zhe Jia
    Acta mathematica scientia,Series B    2024, 44 (3): 909-924.   DOI: 10.1007/s10473-024-0308-7
    Abstract70)            Save
    This paper is concerned with the following attraction-repulsion chemotaxis system with $p$-Laplacian diffusion and logistic source:
    $$\left\{\begin{array}{ll}u_{t}=\nabla\cdot(|\nabla u|^{p-2}\nabla u)-\chi \nabla\cdot(u \nabla v)+\xi \nabla\cdot(u \nabla w)+f(u),\;\;\;x\in \Omega,\;t>0,\\v_{t}=\triangle v-\beta v+\alpha u^{k_{1}},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x\in \Omega,\;t>0,\\0=\triangle w-\delta w+\gamma u^{k_{2}},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x\in \Omega,\;t>0,\\u(x,0)=u_{0}(x),\;\;v(x,0)=v_{0}(x),\;\;w(x,0)=w_{0}(x), \;\;\;\;\;\;\;\;\;\;\;\;\;x\in \Omega.\end{array}\right.$$
    The system here is under a homogenous Neumann boundary condition in a bounded domain $ \Omega \subset \mathbb{R}^{n}(n\geq2) $, with $ \chi, \xi, \alpha,\beta,\gamma,\delta, k_{1}, k_{2} >0, p\geq 2$. In addition, the function $f$ is smooth and satisfies that $f(s)\leq\kappa-\mu s^{l}$ for all $s\geq0$, with $\kappa\in \mathbb{R}, \mu>0, l>1$. It is shown that (i) if $l>\max\{ 2k_{1}, \frac{2k_{1}n}{2+n}+\frac{1}{p-1}\}$, then system possesses a global bounded weak solution and (ii) if $k_{2}>\max\{2k_{1}-1, \frac{2k_{1}n}{2+n}+\frac{2-p}{p-1}\}$ with $l>2$, then system possesses a global bounded weak solution.
    Reference | Related Articles | Metrics
    TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE*
    Lixia Feng, Yan Li, Zhiyu Wang, Liankuo Zhao
    Acta mathematica scientia,Series B    2024, 44 (5): 1707-1720.   DOI: 10.1007/s10473-024-0504-5
    Abstract70)            Save
    In this paper, by characterizing Carleson measures, we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békollé weights over the half-plane for all index choices.
    Reference | Related Articles | Metrics
    ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK*
    Shuxiong Zhang, Jie Xiong
    Acta mathematica scientia,Series B    2024, 44 (5): 2051-2072.   DOI: 10.1007/s10473-024-0525-0
    Abstract68)            Save
    Let $\{Z_n\}_{n\geq 0 }$ be a critical or subcritical $d$-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on $\mathbb{R}^d$. Denote by $R_n:=\sup\{u>0:Z_n(\{x\in\mathbb{R}^d:|x|<u\})=0\}$ the radius of the largest empty ball centered at the origin of $Z_n$. In this work, we prove that after suitable renormalization, $R_n$ converges in law to some non-degenerate distribution as $n\to\infty$. Furthermore, our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk. This completes the results of Révész [13] for the critical binary branching Wiener process.
    Reference | Related Articles | Metrics