A Note on Rough Parametric Marcinkiewicz Functions

Laith Hawawsheh; Ahmad Al-Salman; Shaher Momani

doi:10.4208/ata.OA-2017-0074

A Note on Rough Parametric Marcinkiewicz Functions

Laith Hawawsheh
, Ahmad Al-Salman
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

German Iordanian University
Sultan Qaboos University
University of Jordan

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

2 Scopus citations

Abstract

In this note, we obtain sharp Westimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L¹(S^n-1).

Original language	English
Pages (from-to)	52-59
Number of pages	8
Journal	Analysis in Theory and Applications
Volume	36
Issue number	1
DOIs	https://doi.org/10.4208/ata.OA-2017-0074
State	Published - 2020

Keywords

Fourier transform
Marcinkiewicz integrals
Marcinkiewicz interpolation theorem
parametric Marcinkiewicz functions
rough kernels

Access to Document

10.4208/ata.OA-2017-0074

Cite this

@article{f90dc6df2045466c8e4d95d3646e00c2,

title = "A Note on Rough Parametric Marcinkiewicz Functions",

abstract = "In this note, we obtain sharp Westimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L1(Sn-1).",

keywords = "Fourier transform, Marcinkiewicz integrals, Marcinkiewicz interpolation theorem, parametric Marcinkiewicz functions, rough kernels",

author = "Laith Hawawsheh and Ahmad Al-Salman and Shaher Momani",

note = "Publisher Copyright: {\textcopyright} 2020 Global-Science Press.",

year = "2020",

doi = "10.4208/ata.OA-2017-0074",

language = "English",

volume = "36",

pages = "52--59",

journal = "Analysis in Theory and Applications",

issn = "1672-4070",

publisher = "Global Science Press",

number = "1",

}

TY - JOUR

T1 - A Note on Rough Parametric Marcinkiewicz Functions

AU - Hawawsheh, Laith

AU - Al-Salman, Ahmad

AU - Momani, Shaher

PY - 2020

Y1 - 2020

N2 - In this note, we obtain sharp Westimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L1(Sn-1).

AB - In this note, we obtain sharp Westimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L1(Sn-1).

KW - Fourier transform

KW - Marcinkiewicz integrals

KW - Marcinkiewicz interpolation theorem

KW - parametric Marcinkiewicz functions

KW - rough kernels

UR - https://www.scopus.com/pages/publications/105011740686

U2 - 10.4208/ata.OA-2017-0074

DO - 10.4208/ata.OA-2017-0074

M3 - Article

AN - SCOPUS:105011740686

SN - 1672-4070

VL - 36

SP - 52

EP - 59

JO - Analysis in Theory and Applications

JF - Analysis in Theory and Applications

IS - 1

ER -

A Note on Rough Parametric Marcinkiewicz Functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this