On weak type inequalities for rare maximal functions

K. Hare; A. Stokolos

ArticleOriginal scientific text

Title

On weak type inequalities for rare maximal functions

Authors ¹, ²

Affiliations

Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Department of Mathematics, Odessa State University, Petra Velikogo, 2 270000 Odessa, Ukraine

Abstract

The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.

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P. L. Ul'yanov, Embedding of some function classes $H^{ω}_p$ , Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 649-686 (in Russian).

Title

On weak type inequalities for rare maximal functions

Affiliations

Abstract

Bibliography