Publicacions Matemàtiques

Local maximal operators on measure metric spaces

Chin-Cheng Lin, Krzysztof Stempak, and Ya-Shu Wang

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Abstract

The notion of local maximal operators and objects associated to them is introduced and systematically studied in the general setting of measure metric spaces. The locality means here some restrictions on the radii of involved balls. The notion encompasses different definitions dispersed throughout the literature. One of the aims of the paper is to compare properties of the 'local' objects with the 'global' ones (i.e. these with no restrictions on the radii of balls). An emphasis is put on the case of locality function of Whitney type. Some aspects of this specific case were investigated earlier by two out of three authors of the present paper.

Article information

Source
Publ. Mat., Volume 57, Number 1 (2013), 239-264.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.pm/1355854305

Mathematical Reviews number (MathSciNet)
MR3058934

Zentralblatt MATH identifier
1291.42015

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory 51F99: None of the above, but in this section

Keywords
Local maximal operators measure metric spaces locality functions of Whitney type local $A_p$ weights local $\mathit{BMO}$ spaces

Citation

Lin, Chin-Cheng; Stempak, Krzysztof; Wang, Ya-Shu. Local maximal operators on measure metric spaces. Publ. Mat. 57 (2013), no. 1, 239--264. https://projecteuclid.org/euclid.pm/1355854305


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