Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (4): 1618-1632.doi: 10.1007/s10473-023-0411-1
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Guoen HU†, Jie LIU
Received:
2022-04-17
Revised:
2022-06-27
Published:
2023-08-08
Contact:
†Guoen HU, E-mail: About author:
Jie LIU, E-mail: 57923206@qq.com
Supported by:
Guoen HU, Jie LIU. BOUNDEDNESS OF THE CALDERÓN COMMUTATOR WITH A ROUGH KERNEL ON TRIEBEL-LIZORKIN SPACES∗[J].Acta mathematica scientia,Series B, 2023, 43(4): 1618-1632.
[1] Calderón A P. Commutators of singular integral operators. Proc Nat Acad Sci USA,1965, 53: 1092-1099 [2] Chen J, Hu G, Tao X. $L^p(\mathbb{R}^d)$ boundedness for the Calderón commutator with rough kernel. J Geom Anal,2023, 33: Art 14 [3] Chen Y, Ding Y, Hong G, Xiao J.Some jump and variational inequalities for the Calderón commutators and related operators. arxiv:1709.03127 [4] Ding Y, Lai X. Weak type (1,1) bounded criterion for singular integral with rough kernel and its applications. Trans Amer Math Soc, 2019, 371: 1649-1675 [5] Duoandikoetxea J.Extrapolation of weights revisited: new proofs and sharp bounds. J Function Anal, 2011, 260: 1886-1901 [6] Fan D, Zhao F. Littlewood-Paley functions and Triebel-Lizorkin spaces and Besov spaces. Appl Theory Appl2021, 37: 267-288 [7] Fefferman C, Stein E M. Some maximal inequalities. Amer J Math, 1971, 93: 107-115 [8] Grafakos L. Modern Fourier Analysis. New York: Springer, 2008 [9] Han Y, Sawyer E T. Para-accretive functions, the weak boundedness properties and the $Tb$ theorem. Rev Mat Iberoam, 1990, 6: 17-41 [10] Hofmann S. Weighted norm inequalities for commutators of rough singular integrals. Indiana Univ Math J, 1990, 39: 1275-1304 [11] Pan Y, Wu Q, Yang D. A remark on multilinear singular integrals with rough kernels. J Math Anal Appl, 2001, 253: 310-321 |
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