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ON A DISCRETE VERSION OF TANAKA'S THEOREM FOR MAXIMAL FUNCTIONS.
- Source :
-
Proceedings of the American Mathematical Society . May2012, Vol. 140 Issue 5, p1669-1680. 12p. - Publication Year :
- 2012
-
Abstract
- In this paper we prove a discrete version of Tanaka's theorem for the Hardy-Littlewood maximal operator in dimension n = 1, both in the noncentered and centered cases. For the non-centered maximal operator Μ M we prove that, given a function f : Z → R of bounded variation, Var(Mf) ≤ Var(f), where Var(f) represents the total variation of f. For the centered maximal operator M we prove that, given a function f : Z → R such that f ϵ Μ1(Z), Var(Mf) ≤ C‖f‖Μе1(Z). This provides a positive solution to a question of HajΜlasz and Onninen in the discrete one-dimensional case. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 140
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 70547578
- Full Text :
- https://doi.org/10.1090/S0002-9939-2011-11008-6