## Abstract Our aim in this paper is to deal with integrability of maximal functions for generalized Lebesgue spaces with variable exponent. Our exponent approaches 1 on some part of the domain, and hence the integrability depends on the shape of that part and the speed of the exponent approaching
Iterated maximal functions in variable exponent Lebesgue spaces
✍ Scribed by Petteri Harjulehto; Peter Hästö; Yoshihiro Mizuta; Tetsu Shimomura
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 229 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0025-2611
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract This article contains results about the boundedness of the Hardy–Littlewood maximal operator in variable exponent Lebesgue spaces. We study the situation where the exponent approaches one in some parts of the domain. We show that the boundedness depends on how fast the exponent approach
We consider generalized potential operators with the kernel a ([ (x ,y )]) [ (x ,y )] N on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ≤ Kr N , N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity w