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Rough Marcinkiewicz integrals along certain smooth curves
Frontiers of Mathematics in China, 2012Let \(\Omega \in L^1(S^{m-1} \times S^{n-1})\) be satisfying \(\Omega(sx,ty)=\Omega(x,y)\) for \(s,t>0\) and \[ \int_{S^{m-1}}\Omega(u',\cdot)d\sigma(u') = \int_{S^{n-1}}\Omega(\cdot, v')d\sigma(v') =0. \] For suitable functions \(\varphi, \psi: {\mathbb R}^+ \to {\mathbb R}\), the multiple Marcinkiewicz integral operator is defined by \[ {\mathcal{M ...
Ma, Bolin, Wu, Huoxiong, Zhao, Xiating
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Marcinkiewicz integral operators on product domains
Mathematical Proceedings of the Cambridge Philosophical Society, 2002With the cancellation property of the bounded kernel, we prove that the generalized Marcinkiewicz integral operator is bounded on L2 (ℝn×ℝm) for all dimensions n, m.
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On Marcinkiewicz Integral Operators with Rough Kernels
Integral Equations and Operator Theory, 2005This paper is devoted to the study on the L p -mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on $$\mathbb{R}^n .$$ The
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Entropy numbers and Marcinkiewicz-type discretization
Journal of Functional Analysis, 2021Feng Dai, Andriy Prymak, Sergey Tikhonov
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Completely continuous commutator of Marcinkiewicz integral
Publicationes Mathematicae Debrecen, 2017Jiecheng Chen, Guoen Hu
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A NOTE ON MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION
Journal of the Australian Mathematical Society, 2018Feng Liu
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A problem on rough parametric Marcinkiewicz functions
Journal of the Australian Mathematical Society, 2002Shanzhen Lu
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Integral operators of Marcinkiewicz type on Triebel–Lizorkin spaces
Mathematische Nachrichten, 2017Feng Liu
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Marcinkiewicz estimates for solution to fractional elliptic Laplacian equation
Computers and Mathematics With Applications, 2019Shuibo Huang, Qiaoyu Tian
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