Strong convergence theorems for Hp(double-struct T sign x ⋯ x double-struct T sign)

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Multiplier operators on the Hardy space Hp(double-struct T sign x ⋯ x double-struct T sign) are investigated and Bernstein's inequality for multi-parameter trigonometric polynomials is verified. We prove that certain means of the partial sums of the multi-parameter trigonometric Fourier series are uniformly bounded operators from Hp(double-struct T sign x ⋯ x double-struct T sign) to Lp (1/2 <p ≤ 1). As a consequence we obtain strong convergence theorems concerning the partial sums. The dual inequalities are also verified and a Marcinkiewicz - Zygmund type inequalities is obtained for the BMO(double-struct T sign x ⋯ x double-struct T sign) spaces.

Original languageEnglish
Pages (from-to)667-678
Number of pages12
JournalPublicationes Mathematicae
Volume58
Issue number4
Publication statusPublished - 2001

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Strong Theorems
Strong Convergence
Convergence Theorem
Partial Sums
Bernstein Inequality
Trigonometric Series
Trigonometric Polynomial
Bounded Operator
Hardy Space
Fourier series
Multiplier
Operator

Keywords

  • Bernstein's inequality
  • Hardy spaces
  • Multiplier operators
  • Strong means

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Strong convergence theorems for Hp(double-struct T sign x ⋯ x double-struct T sign). / Weisz, F.

In: Publicationes Mathematicae, Vol. 58, No. 4, 2001, p. 667-678.

Research output: Contribution to journalArticle

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