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On Hardy - Littlewood Maximal Functions in Orlicz Spaces

✍ Scribed by H. Kita

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
664 KB
Volume
183
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lim~s~→ ∞ b(s) = + ∞. Then the following statements for the Hardy ‐ Littlewood maximal function M f (x) are equivalent:
(i) there exist positive constants c~1~ and s~0~ such that magnified image

(ii) there exist positive constant c~2~ and c~3~ such thatmagnified image

.

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