Journal article

### On a discrete version of Tanaka's theorem for maximal functions

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 M we prove that, given a function f: Z → R of bounded variation, =, 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 ∈ ł1(Z), =. This provides a positive solution to a question of Hajłlasz and Onninen ...

### Authors

Journal:
Proceedings of the American Mathematical Society
Volume:
140
Issue:
5
Pages:
1669-1680
Publication date:
2012-05-05
DOI:
EISSN:
1088-6826
ISSN:
0002-9939
URN:
uuid:2da1337e-4796-4c9f-a2a4-f8475588f710
Source identifiers:
332544
Local pid:
pubs:332544
Language:
English
Keywords: