A Note on Rough Parametric Marcinkiewicz Functions

In this note,we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators.Our result resolves a long standing open problem.Also,we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L1 (Sn-1).

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Bibliographic Details
Published in:Analysis in theory & applications 2020-01, Vol.36 (1), p.52-59
Main Authors: Laith Hawawsheh, Laith Hawawsheh, Ahmad Al-Salman, Ahmad Al-Salman, Shaher Momani, Shaher Momani
Format: Article
Language:English
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Summary:In this note,we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators.Our result resolves a long standing open problem.Also,we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L1 (Sn-1).
ISSN:1672-4070
1573-8175
DOI:10.4208/ata.OA-2017-0074