## 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
Maximal function on generalized martingale Lebesgue spaces with variable exponent
โ Scribed by Nakai, Eiichi; Sadasue, Gaku
- Book ID
- 122764066
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 348 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0167-7152
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๐ SIMILAR VOLUMES
We consider generalized potential operators with the kernel a ([ (x ,y )]) [ (x ,y )] N on bounded quasimetric measure space (X, ฮผ, d) with doubling measure ฮผ satisfying the upper growth condition ฮผB(x, r) โค Kr N , N โ (0, โ). Under some natural assumptions on a(r) in terms of almost monotonicity w
## Abstract This article contains results about the boundedness of the HardyโLittlewood 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