A generalization for Fourier transforms of a theorem due to Marcinkiewicz

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p0

01(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0

Original languageEnglish
Pages (from-to)675-695
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume252
Issue number2
Publication statusPublished - Dec 15 2000

Fingerprint

Fourier transform
Fourier transforms
Converge
Tempered Distribution
Maximal Operator
Theorem
Norm
Generalization

Keywords

  • Atomic decomposition
  • Hardy spaces
  • Interpolation
  • Marcinkiewicz means
  • p-atom

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

A generalization for Fourier transforms of a theorem due to Marcinkiewicz. / Weisz, F.

In: Journal of Mathematical Analysis and Applications, Vol. 252, No. 2, 15.12.2000, p. 675-695.

Research output: Contribution to journalArticle

@article{da6c7945ba8d4ff5ada971df2fea7fb2,
title = "A generalization for Fourier transforms of a theorem due to Marcinkiewicz",
abstract = "It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p001(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0",
keywords = "Atomic decomposition, Hardy spaces, Interpolation, Marcinkiewicz means, p-atom",
author = "F. Weisz",
year = "2000",
month = "12",
day = "15",
language = "English",
volume = "252",
pages = "675--695",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - A generalization for Fourier transforms of a theorem due to Marcinkiewicz

AU - Weisz, F.

PY - 2000/12/15

Y1 - 2000/12/15

N2 - It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p001(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0

AB - It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p001(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0

KW - Atomic decomposition

KW - Hardy spaces

KW - Interpolation

KW - Marcinkiewicz means

KW - p-atom

UR - http://www.scopus.com/inward/record.url?scp=0034670551&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034670551&partnerID=8YFLogxK

M3 - Article

VL - 252

SP - 675

EP - 695

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -