A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R

Salem Ben Saïd; Luc Deleaval

doi:10.1007/s12220-019-00183-6

A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R

Salem Ben Saïd
, Luc Deleaval

Department of Mathematical Sciences

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

9 Citations (Scopus)

Abstract

In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.

Original language	English
Pages (from-to)	2273-2289
Number of pages	17
Journal	Journal of Geometric Analysis
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s12220-019-00183-6
Publication status	Published - Apr 1 2020

Keywords

Generalized Fourier transform
Hardy–Littlewood maximal theorem
Maximal function

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s12220-019-00183-6

Cite this

@article{62b8d39bf98d4c64b2f2204f7b92c062,

title = "A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R",

abstract = "In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.",

keywords = "Generalized Fourier transform, Hardy–Littlewood maximal theorem, Maximal function",

author = "Salem Ben Sa{\"i}d and Luc Deleaval",

note = "Publisher Copyright: {\textcopyright} 2019, Mathematica Josephina, Inc.",

year = "2020",

month = apr,

day = "1",

doi = "10.1007/s12220-019-00183-6",

language = "English",

volume = "30",

pages = "2273--2289",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R

AU - Ben Saïd, Salem

AU - Deleaval, Luc

PY - 2020/4/1

Y1 - 2020/4/1

N2 - In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.

AB - In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.

KW - Generalized Fourier transform

KW - Hardy–Littlewood maximal theorem

KW - Maximal function

UR - https://www.scopus.com/pages/publications/85073793790

UR - https://www.scopus.com/pages/publications/85073793790#tab=citedBy

U2 - 10.1007/s12220-019-00183-6

DO - 10.1007/s12220-019-00183-6

M3 - Article

AN - SCOPUS:85073793790

SN - 1050-6926

VL - 30

SP - 2273

EP - 2289

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

ER -

A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this