ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

doi:10.1007/s10473-021-0114-4

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (1): 241-256.doi: 10.1007/s10473-021-0114-4

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ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

Ronghui LIU¹, Feng LIU², Huoxiong WU¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Received:2019-10-09 Revised:2020-01-05 Online:2021-02-25 Published:2021-04-06
Contact: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
About author:Ronghui LIU,E-mail:liuronghuimath@126.com;Feng LIU,E-mail:FLiu@sdust.edu.cn
Supported by:
The authors were partly supported by the NSFC (11771358, 11701333, 11871101).

Abstract

CLC Number:

42B20

Ronghui LIU, Feng LIU, Huoxiong WU. ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS[J].Acta mathematica scientia,Series B, 2021, 41(1): 241-256.

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[1] Al-Salman A, Al-Qassem H, Cheng L C, Pan Y. L^p bounds for the function of Marcinkiewicz. Math Res Lett, 2002, 9(5/6):697-700
[2] Benedek A, Calderón A, Panzone R. Convolution operators on Banach space value functions. Proc Nat Acd Sci USA, 1962, 48:356-365
[3] Cacciafesta F, D'Ancona P. Endpoint estimates and global existence for the nonlinear Dirac equation with potential. J Differential Equations, 2013, 254(5):2233-2260
[4] Cacciafesta F, Lucà R. Singular integrals with angular regularity. Proc Amer Math Soc, 2016, 144:3413-3418
[5] Chen J, Fan D, Pan Y. A note on a Marcinkiewicz integral operator. Math Nachr, 2001, 227:33-42.
[6] Córdoba A. Singular integrals and maximal functions:the disk miltiplier revisited. Adv Math, 2016, 290:208-235
[7] D'Ancona P, Lucà R. On the regularity set and angular integrability for the Navier-Stokes equation. Arch Rational Mech Anal, 2016, 221:1255-1284
[8] Ding Y, Fan D, Pan Y. L^p-boundedness of Marcinkiewicz integrals with Hardy space function kernel. Acta Math Sin (Engl Ser), 2000, 16:593-600
[9] Ding Y, Lu S, Yabuta K. A problem on rough Marcinkiewicz functions. J Austral Math Soc, 2001, 71:1-9
[10] Duoandikoetxea J, Rubio de Francia J L. Maximal and singular integral operators via Fourier transform estimates. Invent Math, 1986, 84:541-561
[11] Fan D, Pan Y. Singular integral operators with rough kernels supported by subvarieties. Amer J Math, 1997, 119:799-839
[12] Fan D, Sato S. A note on the singular integrals associated with a variable surface of revolution. Math Inequal Appl, 2009, 12(2):441-454
[13] Fang D, Wang C. Weighted Strichartz estimates with angular regularity and their applications. Forum Math, 2011, 23:181-205
[14] Grafakos L, Stefanov A. L^p bounds for singular integrals and maximal singular integrals with rough kernels. Indiana Univ Math J, 1998, 47(2):455-469
[15] Hofmann S. Weighted norm inequalities and vector valued inequalities for certain rough operators. Indiana Univ Math J, 1993, 42(1):1-14
[16] Hou X, Wu H. Limiting weak-type behaviors for certain Littlewood-Paley functions. Acta Math Sci, 2019, 39B(1):11-25
[17] Liu F. Weighted estimates for Marcinkiewicz integrals with applications to angular integrability. 2019, preprint.
[18] Liu F, Fan D. Weighted estimates for rough singualr integrals with applications to angular integrability. Pacific J Math, 2019, 301(1):267-295
[19] Liu F, Wu H, Zhang D. L^p bounds for parametric Marcinkiewicz integrals with mixed homogeneity. Math Inequal Appl, 2015, 8(2):453-469
[20] Liu F, Liu R, Wu H. Weighted estiamtes for rough singular integrals with applications to angular integrablity, Ⅱ. Math Inequal Appl, 2020, 23(1):393-418
[21] Liu R, Liu F, Wu H. Mixed radial-angular integrability for rough singular integrals and maximal operators. Proc Amer Math Soc, 2020, 148(9):3943-3956
[22] Li W, Si Z, Yabuta K. Boundedness of singular integrals associated to surfaces of revolution on Triebel Lizorkin spaces. Forum Math, 2016, 28(1):57-75
[23] Stein E M. On the function of Littlewood-Paley, Lusin and Marcinkiewicz. Trans Amer Math Soc, 1958, 88:430-466
[24] Sterbenz J. Angular regularity and Strichartz estimates for the wave equation. Inter Math Res Not, 2005, 4:187-231
[25] Tao T. Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation. Comm Partial Differential Equations, 2000, 25(7/8):1471-1485
[26] Walsh T. On the function of Marcinkiewicz. Studia Math, 1972, 44:203-217
[27] Wu H. On Marcinkiewicz integral operators with rough kernels. Integral Equations Operator Theory, 2005, 52:285-298
[28] Wu H. L^p bounds for Marcinkiewicz integrals associated to surfaces of revolution. J Math Anal Appl, 2006, 321(2):811-827
[29] Wu H, Xu J. Rough Marcinkiewicz integrals associated to surfaces of revolution on product domains. Acta Math Sci, 2009, 29B(2):294-304

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

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