Generalization of Hardy–Littlewood maximal inequality with variable exponent

Ferenc Weisz

Mathematische Nachrichten, 2023, vol. 296, issue 4, 1687-1705

Abstract: Let p(·)$p(\cdot )$ be a measurable function defined on Rd${\mathbb {R}}^d$ and p−:=infx∈Rdp(x)$p_-:=\inf _{x\in {\mathbb {R}}^d}p(x)$. In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone‐like set defined by a given function ψ. Moreover, instead of the integral means, we consider the Lq(·)$L_{q(\cdot )}$‐means. Let p(·)$p(\cdot )$ and q(·)$q(\cdot )$ satisfy the log‐Hülder condition and p(·)=q(·)r(·)$p(\cdot )= q(\cdot ) r(\cdot )$. Then, we prove that the maximal operator is bounded on Lp(·)$L_{p(\cdot )}$ if 1

Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200188

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:296:y:2023:i:4:p:1687-1705

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().