(C, α) means of d-dimensional trigonometric-Fourier series

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The d-dimensional classical Hardy spaces H p(T d) are introduced and it is shown that the maximal operator of the (C, α) (α = (α 1,... , α d)) means of a distribution is bounded from H p(T d) to L p(T d) (d/(d + 1), 1/(α k + 1) <p <∞) provided that the supremum in the maximal operator is taken over a positive cone. Moreover, we prove that the (C, α) means are uniformly bounded on the spaces H p(T d) whenever d/(d+ 1), 1/(α k + 1) <p <∞. Thus, in case f ∈ H p(T), the Cesàro means converge to f in H p(T d) norm (d/(d + 1), 1/(α k + 1) <p <∞). The same results are proved for the conjugate (C, α) means, too.

Original languageEnglish
Pages (from-to)705-720
Number of pages16
JournalPublicationes Mathematicae
Volume52
Issue number3-4
Publication statusPublished - 1998

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Trigonometric Series
Fourier series
Maximal Operator
Positive Cone
H-space
Hardy Space
Supremum
Converge
Norm

Keywords

  • (C, α) summability
  • Atomic decomposition
  • Conjugate function
  • Hardy spaces
  • Interpolation
  • p-atom

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

(C, α) means of d-dimensional trigonometric-Fourier series. / Weisz, F.

In: Publicationes Mathematicae, Vol. 52, No. 3-4, 1998, p. 705-720.

Research output: Contribution to journalArticle

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