The maximal operator on weighted variable Lebesgue spaces

By D. Cruz-Uribe, Lars Diening, P. Hasto. 2011

161 citations recorded by the source corpus.

We study the boundedness of the maximal operator on the weighted variable exponent Lebesgue spaces Lωp(·) (Ω). For a given log-Hölder continuous exponent p with 1 < inf p ⩽ supp < ∞ we present a necessary and sufficient condition on the weight ω for the boundedness of M. This condition is a generalization of the classical Muckenhoupt condition.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c71e729749a5dc05b0912fb5cd5670fc931d9d9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Ciqiang Zhuo
4. Yiyu Liang
5. L. Wang
6. Iwona Chlebicka
7. Yoshihiro Sawano
8. D. Cruz-Uribe

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Ciqiang Zhuo
4. Yiyu Liang
5. Yoshihiro Sawano
6. D. Cruz-Uribe
7. Iwona Chlebicka
8. L. Wang

Citations in the corpus

• Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, methodology): “These spaces were introduced by Birnbaum-Orlicz [3] and Orlicz [34], and widely used in the study of harmonic analysis as well as partial differential equations; see, for example, [1, 2, 6, 7, 8, 11, 12, 13, 14, 20, 30, 43, 48, 50].”
• Extrapolation and weighted norm inequalities in the variable Lebesgue spaces (2014, background): “Weighted norm inequalities for the maximal operator in the variable Lebesgue spaces were proved in [12, 16, 24] (see also [25] for related results).”
• A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “from the point of view of harmonic analysis in [65].”
• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “ articles [31] of Kov´aˇcik and Ra´kosn´ık as well as [8] of Cruz-Uribe and [13] of Diening. The variable Lebesgue spaces have already widely used in the study of harmonic analysis; see, for example, [10, 9, 11, 14, 15, 48, 26]. Apart from theoretical considerations, such function spaces have intere”
• Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, methodology): “ modern development was started with the article [37] of Kova´ˇcik and Ra´kosn´ık in 1991 and widely used in the study of harmonic analysis as well as partial differential equations; see, for example, [6, 12, 13, 14, 17, 18, 19, 21, 32, 48]. The motivation to study such function spaces also comes fro”