Limiting Weak-Type Behaviors for Fractional Maximal Operators and Fractional Integrals with Rough Kernel

By a reduction method, the limiting weak-type behaviors of fractional maximal operators and fractional integrals are established without any smoothness assumption on the kernel, which essentially improve and extend previous results. As a byproduct, we characterize the boundedness of several operator...

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Bibliographic Details
Published in:	Mediterranean journal of mathematics Vol. 19; no. 2
Main Authors:	Zhao, Guoping, Guo, Weichao
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-04-2022 Springer Nature B.V
Subjects:	Constraining Fractional calculus Integrals Kernels Mathematics Mathematics and Statistics Operators Smoothness Limiting behaviors maximal operators 42B25 weak type estimates fractional integrals 42B20
Online Access:	Get full text
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Summary:	By a reduction method, the limiting weak-type behaviors of fractional maximal operators and fractional integrals are established without any smoothness assumption on the kernel, which essentially improve and extend previous results. As a byproduct, we characterize the boundedness of several operators by the membership of their kernel in Lebesgue space on sphere.
ISSN:	1660-5446 1660-5454
DOI:	10.1007/s00009-022-02021-6