On integrability of functions defined by trigonometric series

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2 Citations (Scopus)

Abstract

The goal of the present paper is to generalize two theorems of R.P. Boas Jr. pertaining to Lp (p > 1) integrability of Fourier series with nonnegative coefficients and weight xγ. In our improvement the weight xγ is replaced by a more general one, and the case p = 1 is also yielded. We also generalize an equivalence statement of Boas utilizing power-monotone sequences instead of {nγ}.

Original languageEnglish
Article number69
JournalJournal of Inequalities in Pure and Applied Mathematics
Volume9
Issue number3
Publication statusPublished - Nov 3 2008

Keywords

  • Equivalence of coefficient conditions
  • L integrability
  • Quasi power-monotone sequences
  • Sine and cosine series

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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