Bounded operators on weak Hardy spaces and applications

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

The atomic decomposition of weak Hardy spaces consisting of Vilenkin martingales is formulated. Some sufficient conditions for a sublinear operator T to be bounded from the weak Hardy space wHp to the weak wLp space are given. As applications a weak version of the Hardy-Littlewood inequality is obtained and it is shown that the maximal operator of the Cesàro means of a Vilenkin-Fourier series is bounded from wHp to wLp and is of weak type (1, 1). This yields that the Cesàro means of a function f ∈ L1 converge a.e. to the function in question, provided that the Vilenkin system is bounded.

Original languageEnglish
Pages (from-to)249-264
Number of pages16
JournalActa Mathematica Hungarica
Volume80
Issue number3
Publication statusPublished - Aug 1998

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Bounded Operator
Hardy Space
Hardy-Littlewood Inequality
Sublinear Operator
Atomic Decomposition
Maximal Operator
Martingale
Fourier series
Converge
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bounded operators on weak Hardy spaces and applications. / Weisz, F.

In: Acta Mathematica Hungarica, Vol. 80, No. 3, 08.1998, p. 249-264.

Research output: Contribution to journalArticle

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