Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 313-314

EXAMPLES OF METRIC MEASURE SPACES RELATED TO MODIFIED HARDY--LITTLEWOOD MAXIMAL OPERATORS

Krzysztof Stempak

Politechnika Wroclawska, Wydzial Matematyki
Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland; Krzysztof.Stempak 'at' pwr.edu.pl

Abstract. We furnish elementary examples of (nondoubling) metric spaces, for which the modified Hardy-Littlewood maximal operators M_k and M^c_k, uncentered and centered, fail to be weak type (1,1) for 1 ≤ k < 3 and 1 ≤ k < 2, respectively.

2010 Mathematics Subject Classification: Primary 42B25.

Key words: Metric measure space, non-doubling measure, modified Hardy-Littlewood maximal operator, weak type (1,1).

Reference to this article: K. Stempak: Examples of metric measure spaces related to modified Hardy-Littlewood maximal operators. Ann. Acad. Sci. Fenn. Math. 41 (2016), 313-314.

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doi:10.5186/aasfm.2016.4119