Marcinkiewicz functions along flat surfaces with hardy space kernels

Ahmad Al-Salman

doi:10.1216/jiea/1181075348

Marcinkiewicz functions along flat surfaces with hardy space kernels

Ahmad Al-Salman^*

^*Corresponding author for this work

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

13 Citations (Scopus)

Abstract

In this paper, we study Marcinkiewicz integral operators along subvarieties determined by flat surfaces with kernels in the Hardy space H¹(S^n-1). We establish the L^p boundedness of our operators under weak convexity assumptions on the surfaces. Moreover, we establish the L^p boundedness of the corresponding Marcinkiewicz integral operators that are related to area integral and Littlewood-Paley g^z.ast;_λ functions. Our results offer substantial improvements of previously known results.

Original language	English
Pages (from-to)	357-373
Number of pages	17
Journal	Journal of Integral Equations and Applications
Volume	17
Issue number	4
DOIs	https://doi.org/10.1216/jiea/1181075348
Publication status	Published - 2005
Externally published	Yes

Keywords

Area integral
Flat curves
Fourier transform
Littlewood-Paley g* functions
Marcinkiewicz integrals
Rough kernels

ASJC Scopus subject areas

Numerical Analysis
Applied Mathematics

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10.1216/jiea/1181075348

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AU - Al-Salman, Ahmad

PY - 2005

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N2 - In this paper, we study Marcinkiewicz integral operators along subvarieties determined by flat surfaces with kernels in the Hardy space H1(Sn-1). We establish the Lp boundedness of our operators under weak convexity assumptions on the surfaces. Moreover, we establish the Lp boundedness of the corresponding Marcinkiewicz integral operators that are related to area integral and Littlewood-Paley gz.ast;λ functions. Our results offer substantial improvements of previously known results.

AB - In this paper, we study Marcinkiewicz integral operators along subvarieties determined by flat surfaces with kernels in the Hardy space H1(Sn-1). We establish the Lp boundedness of our operators under weak convexity assumptions on the surfaces. Moreover, we establish the Lp boundedness of the corresponding Marcinkiewicz integral operators that are related to area integral and Littlewood-Paley gz.ast;λ functions. Our results offer substantial improvements of previously known results.

KW - Area integral

KW - Flat curves

KW - Fourier transform

KW - Littlewood-Paley g functions

KW - Marcinkiewicz integrals

KW - Rough kernels

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EP - 373

JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

IS - 4

ER -

Marcinkiewicz functions along flat surfaces with hardy space kernels

Abstract

Keywords

ASJC Scopus subject areas

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