Singular integral operators and maximal functions with Hardy space kernels

Ahmad Al-Salman

doi:10.3906/mat-2103-7

Singular integral operators and maximal functions with Hardy space kernels

Ahmad Al-Salman^*

^*Corresponding author for this work

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

Abstract

In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on L^p, 1 < p<∞ provided that the compound curves are determined by generalized polynomials and convex increasing functions. The obtained results offer L^p estimates that are not only new but also they generalize as well as improve previously known results.

Original language	English
Pages (from-to)	2211-2224
Number of pages	14
Journal	Turkish Journal of Mathematics
Volume	45
Issue number	5
DOIs	https://doi.org/10.3906/mat-2103-7
Publication status	Published - 2021
Externally published	Yes

Keywords

compound curves
convex functions
Hardy Littlewood maximal function
Hardy space
Singular integrals

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.3906/mat-2103-7

Cite this

@article{a0a02fabd4b74ce2bdc9aefa1d735bd6,

title = "Singular integral operators and maximal functions with Hardy space kernels",

abstract = "In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on Lp, 1 < p<∞ provided that the compound curves are determined by generalized polynomials and convex increasing functions. The obtained results offer Lp estimates that are not only new but also they generalize as well as improve previously known results.",

keywords = "compound curves, convex functions, Hardy Littlewood maximal function, Hardy space, Singular integrals",

author = "Ahmad Al-Salman",

note = "Publisher Copyright: {\textcopyright} 2021",

year = "2021",

doi = "10.3906/mat-2103-7",

language = "English",

volume = "45",

pages = "2211--2224",

journal = "Turkish Journal of Mathematics",

issn = "1300-0098",

publisher = "TUBITAK",

number = "5",

}

TY - JOUR

T1 - Singular integral operators and maximal functions with Hardy space kernels

AU - Al-Salman, Ahmad

PY - 2021

Y1 - 2021

N2 - In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on Lp, 1 < p<∞ provided that the compound curves are determined by generalized polynomials and convex increasing functions. The obtained results offer Lp estimates that are not only new but also they generalize as well as improve previously known results.

AB - In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on Lp, 1 < p<∞ provided that the compound curves are determined by generalized polynomials and convex increasing functions. The obtained results offer Lp estimates that are not only new but also they generalize as well as improve previously known results.

KW - compound curves

KW - convex functions

KW - Hardy Littlewood maximal function

KW - Hardy space

KW - Singular integrals

UR - http://www.scopus.com/inward/record.url?scp=85115811310&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85115811310&partnerID=8YFLogxK

U2 - 10.3906/mat-2103-7

DO - 10.3906/mat-2103-7

M3 - Article

AN - SCOPUS:85115811310

SN - 1300-0098

VL - 45

SP - 2211

EP - 2224

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 5

ER -

Singular integral operators and maximal functions with Hardy space kernels

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this