Marcinkiewicz integral operators along twisted surfaces

Ahmad Al-Salman

doi:10.3934/cpaa.2021173

Marcinkiewicz integral operators along twisted surfaces

Ahmad Al-Salman^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Marcinkiewicz integral operators on product domains defined by translates determined by twisted surfaces are introduced. Maximal functions along twisted surfaces are also introduced. Conditions on the underlined surfaces implying that the corresponding Marcinkiewicz integral operators map L^p → Lp for 1 < p < ∞ are obtained. A general method involving lacunary families of multi-indices is developed.

Original language	English
Pages (from-to)	159-181
Number of pages	23
Journal	Communications on Pure and Applied Analysis
Volume	21
Issue number	1
DOIs	https://doi.org/10.3934/cpaa.2021173
Publication status	Published - Jan 2022

Keywords

Fourier transform
Marcinkiewicz integral operators
Product domains
Rough kernels

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2021173

Cite this

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title = "Marcinkiewicz integral operators along twisted surfaces",

abstract = "Marcinkiewicz integral operators on product domains defined by translates determined by twisted surfaces are introduced. Maximal functions along twisted surfaces are also introduced. Conditions on the underlined surfaces implying that the corresponding Marcinkiewicz integral operators map Lp → Lp for 1 < p < ∞ are obtained. A general method involving lacunary families of multi-indices is developed.",

keywords = "Fourier transform, Marcinkiewicz integral operators, Product domains, Rough kernels",

author = "Ahmad Al-Salman",

year = "2022",

month = jan,

doi = "10.3934/cpaa.2021173",

language = "English",

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AB - Marcinkiewicz integral operators on product domains defined by translates determined by twisted surfaces are introduced. Maximal functions along twisted surfaces are also introduced. Conditions on the underlined surfaces implying that the corresponding Marcinkiewicz integral operators map Lp → Lp for 1 < p < ∞ are obtained. A general method involving lacunary families of multi-indices is developed.

KW - Fourier transform

KW - Marcinkiewicz integral operators

KW - Product domains

KW - Rough kernels

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JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 1

ER -

Marcinkiewicz integral operators along twisted surfaces

Abstract

Keywords

ASJC Scopus subject areas

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