Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels
Journal of Inequalities and Applications, 2008 The existence and boundedness on Sobolev spaces and Hardy-Sobolev spaces for the hypersingular Marcinkiewicz integrals with variable kernels are derived.
Songyan Zhang, Xiao Yu, Xiangxing Tao
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Optimal control of singular Fourier multipliers by maximal operators [PDF]
, 2013 We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de Francia--Semmes,
Bennett, Jonathan
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On boundedness of the Hilbert transform on Marcinkiewicz spaces
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 We study boundedness properties of the classical (singular) Hilbert transform (Hf)(t) = p.v.1/π ∫R f(s)/(t − s) ds, acting on Marcinkiewicz spaces. The Hilbert transform is a linear operator which arises from the study of boundary values of the real and
N.T. Bekbayev, K.S. Tulenov
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Triebel--Lizorkin space estimates for multilinear operators of sublinear operators [PDF]
, 2003 In this paper, we obtain the continuity for some multilinear operators related to certain non-convolution operators on the Triebel--Lizorkin space. The operators include Littlewood--Paley operator and Marcinkiewicz operator.Comment: 15 pages, no figures,
Lanzhe, Liu
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Boundedness of Marcinkiewicz Integrals and Their Commutators on Generalized Weighted Morrey Spaces
Journal of Function Spaces, 2015 We will study the boundedness of Marcinkiewicz integrals with rough kernel on the generalized weighted Morrey spaces. We will also prove that the commutator operators formed by a BMORn function and Marcinkiewicz integrals are also bounded on the ...
Runqing Cui, Zhang Li
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A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type
Journal of Function Spaces, 2018 We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions
Daiqing Zhang
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Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups [PDF]
, 2018 In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs.
Kassymov, Aidyn +2 more
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Almost everywhere convergence of Fej\'er means of two-dimensional triangular Walsh-Fourier series [PDF]
, 2017 In 1987 Harris proved (Proc. Amer. Math.
Gát, György
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Marcinkiewicz积分在加权Campanato空间上的有界性(Marcinkiewicz integrals on weighted Campanato spaces)
Zhejiang Daxue xuebao. Lixue ban, 2008 The Marcinkiewicz integrals are class of important operators in analysis and are widely studied. The boundedness of the Marcinkiewicz integral operator on certain weighted Campanato spaces is estiblished.
SIZeng-yan(司增艳) +1 more
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The multilinear strong maximal function [PDF]
, 2010 A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained.
Grafakos, Loukas +3 more
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