Rough oscillatory singular integral operators of nonconvolution type

Research output: Contribution to journalArticle

5 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 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.

Original languageEnglish
Pages (from-to)72-88
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume299
Issue number1
DOIs
Publication statusPublished - Nov 1 2004

Fingerprint

Oscillatory Singular Integral
Singular Integral Operator
Rough
Mathematical operators
Polynomials
kernel
Polynomial
Operator
Class

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

Cite this

Rough oscillatory singular integral operators of nonconvolution type. / Al-Salman, Ahmad.

In: Journal of Mathematical Analysis and Applications, Vol. 299, No. 1, 01.11.2004, p. 72-88.

Research output: Contribution to journalArticle

@article{5e1ec71f98b0430c8632cac48e681fb6,
title = "Rough oscillatory singular integral operators of nonconvolution type",
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",
year = "2004",
month = "11",
day = "1",
doi = "10.1016/j.jmaa.2004.06.006",
language = "English",
volume = "299",
pages = "72--88",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Rough oscillatory singular integral operators of nonconvolution type

AU - Al-Salman, Ahmad

PY - 2004/11/1

Y1 - 2004/11/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=4644318838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4644318838&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2004.06.006

DO - 10.1016/j.jmaa.2004.06.006

M3 - Article

AN - SCOPUS:4644318838

VL - 299

SP - 72

EP - 88

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -