Maximal operator of the Fejér means of triangular partial sums of two-dimensional WalshFourier series

Ushangi Goginava, F. Weisz

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

It is proved that the maximal operator σδ# of the triangular-Fejér-means of a two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 > p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σδ 2n of a function f ∈ L1 converge a.e. to f . The maximal operator σδ# is bounded from the Hardy space H 1/2 to the space weak-L 1/2 and is not bounded from the Hardy space H 1/2 to the space L 1/2.

Original languageEnglish
Pages (from-to)101-115
Number of pages15
JournalGeorgian Mathematical Journal
Volume19
Issue number1
DOIs
Publication statusPublished - Mar 2012

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Maximal Operator
Partial Sums
Hardy Space
Triangular
Series
L-space
Fourier series
Converge

Keywords

  • Hardy space
  • Maximal operator
  • Triangular partial sums
  • Walsh function

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Maximal operator of the Fejér means of triangular partial sums of two-dimensional WalshFourier series. / Goginava, Ushangi; Weisz, F.

In: Georgian Mathematical Journal, Vol. 19, No. 1, 03.2012, p. 101-115.

Research output: Contribution to journalArticle

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