Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 443-448

MODIFIED HARDY–LITTLEWOOD MAXIMAL OPERATORS ON NONDOUBLING METRIC MEASURE SPACES

Krzysztof Stempak

Politechnika Wroclawska, Instytut Matematyki i Informatyki
Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland; Krzysztof.Stempak@pwr.edu.pl

Abstract. We investigate the modified Hardy–Littlewood maximal operators, uncentered M_kf(x) = sup 1/μ(kB) ∫_B|f|dμ, and centered M_k^cf(x) = sup 1/μ(B(x,kr)) ∫_B(x,r)|f|dμ, k ≥ 1, in the setting of a general measure space (X,d,μ). By using an enhanced version of the basic covering theorem we prove that M₃ and M₂^c are weak type (1,1).

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: Modified Hardy–Littlewood maximal operators on nondoubling metric measure spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 443-448.

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doi:10.5186/aasfm.2015.4024