Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains

Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains

We prove <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> estimates of a class of generalized...

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Bibliographic Details
Main Authors: Mohammed Ali, Hussain Al-Qassem
Format: Article
Language:English
Published: MDPI AG 2023-06-01
Series:Axioms
Subjects:
Triebel–Lizorkin space
rough kernel
parabolic Marcinkiewicz integral
product domains
extrapolation
Online Access:https://www.mdpi.com/2075-1680/12/6/596
Description
Summary:We prove <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula> estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument, we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains.
ISSN:2075-1680

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