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Almost Everywhere Convergence of Fejér Means of L 1 Functions on Rarely Unbounded Vilenkin Groups.
- Source :
- Acta Mathematica Sinica; Dec2007, Vol. 23 Issue 12, p2269-2294, 26p
- Publication Year :
- 2007
-
Abstract
- A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of the Fejér (or ( C, 1)) means of functions on unbounded Vilenkin groups. There are several papers of the author of this paper concerning this. That is, we know the a.e. convergence σ<subscript> n </subscript> f → f ( n → ∞) for functions f ∈ L <superscript> p </superscript>, where p > 1 ( Journal of Approximation Theory, 101(1), 1–36, (1999)) and also the a.e. convergence σ M <subscript> n </subscript> f → f ( n → ∞) for functions f ∈ L <superscript>1</superscript> ( Journal of Approximation Theory, 124(1), 25–43, (2003)). The aim of this paper is to prove the a.e. relation lim<subscript> n </subscript>→ σ <subscript> n </subscript> f = f for each integrable function f on any rarely unbounded Vilenkin group. The concept of the rarely unbounded Vilenkin group is discussed in the paper. Basically, it means that the generating sequence m may be an unbounded one, but its "big elements" are not "too dense". [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 23
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 27500249
- Full Text :
- https://doi.org/10.1007/s10114-007-0961-5