Two-parameter Hardy-Littlewood inequalities

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The inequality (Formula presented) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space Hp on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in Lp whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from H1 converges a.e. and also in L1 norm to that function.

Original languageEnglish
Pages (from-to)175-184
Number of pages10
JournalStudia Mathematica
Volume118
Issue number2
Publication statusPublished - 1996

Fingerprint

Hardy-Littlewood Inequality
Fourier coefficients
Fourier series
Two Parameters
Monotone
Trigonometric Series
L1-norm
Partial Sums
Hardy Space
Supremum
Converge
Arbitrary
Coefficient

Keywords

  • Atomic decomposition
  • Hardy spaces
  • Hardy-Littlewood inequalities
  • Rectangle p-atom

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Two-parameter Hardy-Littlewood inequalities. / Weisz, F.

In: Studia Mathematica, Vol. 118, No. 2, 1996, p. 175-184.

Research output: Contribution to journalArticle

Weisz, F. / Two-parameter Hardy-Littlewood inequalities. In: Studia Mathematica. 1996 ; Vol. 118, No. 2. pp. 175-184.
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