Norms supporting the Lebesgue differentiation theorem-Reference-Cited by-同舟云学术

Norms supporting the Lebesgue differentiation theorem

Published:2017-10-23 Issue:01 Volume:20 Page:1750020
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Cavaliere Paola¹,Cianchi Andrea²,Pick Luboš³,Slavíková Lenka³

Affiliation:

1. Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 84084 Fisciano (SA), Italy

2. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 57/A, 50134 Firenze, Italy

3. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Abstract

A version of the Lebesgue differentiation theorem is offered, where the [Formula: see text] norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue’s theorem holds are characterized.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199717500201

Reference25 articles.

1. Orlicz Spaces and Rearranged Maximal Functions

2. Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces

3. A characteristic of symmetrical spaces

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