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L P (Rn) boundedness for the Marcinkiewicz integral

open access: yesAnalysis in Theory and Applications, 2002
Let \(n\geq 2\) and \(S^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega\) is a homogeneous function of degree zero on \(\mathbb{R}^n\) that satisfies \(\Omega\in L(S^{n-1})\) and \(\int_{S^{n-1}}\Omega\,d\sigma= 0\). Define the Marcinkiewicz integral operator \(\mu_\Omega\)
openaire   +2 more sources

-Boundedness of Marcinkiewicz Integrals along Surfaces with Variable Kernels: Another Sufficient Condition

open access: yesJournal of Inequalities and Applications, 2007
We give the estimates for the Marcinkiewicz integral with rough variable kernels associated to surfaces. More precisely, we give some other sufficient conditions which are different from the conditions known before to warrant that the -boundedness ...
Yabuta Kôzô, Xue Qingying
doaj  

Boundedness of a class of rough maximal functions. [PDF]

open access: yesJ Inequal Appl, 2018
Ali M, Al-Mohammed O.
europepmc   +1 more source

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