Wiener amalgams, Hardy spaces and summability of Fourier series

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

Original languageEnglish
Pages (from-to)419-442
Number of pages24
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume145
Issue number2
DOIs
Publication statusPublished - Sep 2008

Fingerprint

Amalgam
Summability
Hardy Space
Fourier series
Wiener Amalgam Spaces
Wiener Algebra
Herz Space
Almost Everywhere Convergence
Maximal Operator
Summation
Convergence Results
Norm
Imply
Algebra

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Wiener amalgams, Hardy spaces and summability of Fourier series. / Weisz, F.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 145, No. 2, 09.2008, p. 419-442.

Research output: Contribution to journalArticle

@article{6c97feda565d4e0fbbb7dc74c7fd54be,
title = "Wiener amalgams, Hardy spaces and summability of Fourier series",
abstract = "A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.",
author = "F. Weisz",
year = "2008",
month = "9",
doi = "10.1017/S0305004108001448",
language = "English",
volume = "145",
pages = "419--442",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - Wiener amalgams, Hardy spaces and summability of Fourier series

AU - Weisz, F.

PY - 2008/9

Y1 - 2008/9

N2 - A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

AB - A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

UR - http://www.scopus.com/inward/record.url?scp=49549093404&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549093404&partnerID=8YFLogxK

U2 - 10.1017/S0305004108001448

DO - 10.1017/S0305004108001448

M3 - Article

VL - 145

SP - 419

EP - 442

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -