Weak type (1, 1) inequalities for discrete rough maximal functions
The aim of this paper is to show that the discrete maximal function , where N h = { n ∈ ℕ: there exists m ∈ ℕ such that n = ⌊ h ( m )⌋} for an appropriate function h , is of weak type (1, 1). As a consequence, we also obtain a pointwise ergodic theorem along the set N h .
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| Veröffentlicht in: | Journal d'analyse mathématique (Jerusalem) 2015-09, Vol.127 (1), p.247-281 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The aim of this paper is to show that the discrete maximal function
, where
N
h
= {
n
∈ ℕ: there exists
m
∈ ℕ such that
n
= ⌊
h
(
m
)⌋} for an appropriate function
h
, is of weak type (1, 1). As a consequence, we also obtain a pointwise ergodic theorem along the set
N
h
. |
|---|---|
| ISSN: | 0021-7670 1565-8538 |
| DOI: | 10.1007/s11854-015-0030-4 |