Regularity of the Hardy-Littlewood maximal operator on block decreasing functions

• Autorzy: J. M. Aldaz , F. J. Pérez Lázaro
• Języki publikacji: EN

Abstrakty

EN

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the $ℓ_{∞}$-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.

Kategorie tematyczne

• 26B30: Absolutely continuous functions, functions of bounded variation
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 3
• Strony: 253-277

Daty

wydano

2009

Twórcy

autor

J. M. Aldaz

• Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain

autor

F. J. Pérez Lázaro

• Departamento de Matemáticas, y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain

Identyfikatory

DOI

10.4064/sm194-3-3