Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients

Péter Simon, F. Weisz

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Our main result is a Hardy type inequality with respect to the two-parameter Vilenkin system (*) (k=1j=1\f̂(k, J)\p(kj)p-2)1/p ≤ Cp∥f∥Hp** (1/2 <p ≤ 2) where f belongs to the Hardy space Hp** (Gm x Gs) defined by means of a maximal function. This inequality is extended to p > 2 if the Vilenkin-Fourier coefficients of f form a monotone sequence. We show that the converse of (*) also holds for all p > 0 under the monotonicity assumption.

Original languageEnglish
Pages (from-to)231-246
Number of pages16
JournalStudia Mathematica
Volume125
Issue number3
Publication statusPublished - 1997

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Hardy-type Inequality
Monotone Sequences
Fourier coefficients
Converse
Monotonicity
Two Parameters
Form

Keywords

  • Hardy-Littlewood inequality
  • Rectangle p-atoms
  • Two-parameter martingales and Hardy spaces
  • Vilenkin functions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hardy type inequalities for two-parameter Vilenkin-Fourier coefficients. / Simon, Péter; Weisz, F.

In: Studia Mathematica, Vol. 125, No. 3, 1997, p. 231-246.

Research output: Contribution to journalArticle

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