Almost everywhere convergence of a subsequence of the logarithmic means of Vilenkin-Fourier series | Zendy

György Gát | Zendy; Károly Nagy | Zendy

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Almost everywhere convergence of a subsequence of the logarithmic means of Vilenkin-Fourier series

Author(s) -

György Gát,

Károly Nagy

Publication year - 2008

Publication title -

facta universitatis - series electronics and energetics

Language(s) - English

Resource type - Journals

eISSN - 2217-5997

pISSN - 0353-3670

DOI - 10.2298/fuee0803275g

Subject(s) - mathematics , subsequence , fourier series , infimum and supremum , logarithm , almost everywhere , locally integrable function , pure mathematics , series (stratigraphy) , operator (biology) , type (biology) , square integrable function , mathematical analysis , combinatorics , integrable system , paleontology , biochemistry , chemistry , ecology , repressor , gene , transcription factor , bounded function , biology

The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1, 1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1, 1), provided that the supremum in the maximal operator is taken over special indices. The set of Vilenkin polynomials is dense in L1, so by the well-known density argument the logarithmic means t2n(f) converge a.e. to f for all integrable function f. .

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