Rough oscillatory singular integral operators of nonconvolution type

Ahmad Al-Salman

doi:10.1016/j.jmaa.2004.06.006

Rough oscillatory singular integral operators of nonconvolution type

Ahmad Al-Salman^*

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

In this paper, we study a classes of oscillatory singular integral operators of nonconvolution type with phases more general than polynomials. We prove that such operators are bounded on L^p provided their kernels satisfy a very weak condition. In addition, we also study the related truncated oscillatory singular integral operators. Moreover, we present a class of unbounded oscillatory singular integral operators.

Original language	English
Pages (from-to)	72-88
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	299
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2004.06.006
Publication status	Published - Nov 1 2004
Externally published	Yes

Keywords

Block spaces
Hardy-Littlewood maximal function
L estimates
Oscillatory singular integral operators
Rough kernels
Truncated maximal oscillatory singular integrals

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2004.06.006

Cite this

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abstract = "In this paper, we study a classes of oscillatory singular integral operators of nonconvolution type with phases more general than polynomials. We prove that such operators are bounded on Lp provided their kernels satisfy a very weak condition. In addition, we also study the related truncated oscillatory singular integral operators. Moreover, we present a class of unbounded oscillatory singular integral operators.",

keywords = "Block spaces, Hardy-Littlewood maximal function, L estimates, Oscillatory singular integral operators, Rough kernels, Truncated maximal oscillatory singular integrals",

author = "Ahmad Al-Salman",

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AU - Al-Salman, Ahmad

PY - 2004/11/1

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AB - In this paper, we study a classes of oscillatory singular integral operators of nonconvolution type with phases more general than polynomials. We prove that such operators are bounded on Lp provided their kernels satisfy a very weak condition. In addition, we also study the related truncated oscillatory singular integral operators. Moreover, we present a class of unbounded oscillatory singular integral operators.

KW - Block spaces

KW - Hardy-Littlewood maximal function

KW - L estimates

KW - Oscillatory singular integral operators

KW - Rough kernels

KW - Truncated maximal oscillatory singular integrals

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DO - 10.1016/j.jmaa.2004.06.006

M3 - Article

AN - SCOPUS:4644318838

SN - 0022-247X

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SP - 72

EP - 88

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Rough oscillatory singular integral operators of nonconvolution type

Abstract

Keywords

ASJC Scopus subject areas

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