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Zeitschrift für Analysis und ihre Anwendungen


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Volume 29, Issue 4, 2010, pp. 401–412
DOI: 10.4171/ZAA/1414

Published online: 2010-10-02

A Characterization of Some Weighted Norm Inequalities for Maximal Operators

Tengiz Kopaliani[1]

(1) Tbilisi State University, Georgia

It is found class of pairs of exponents (p(·), q(·)) such that for pairs of Banach function spaces (Lp(·)(ℝn), Lq(·)(ℝn)) weak Minkowski’s inequality holds. Also some conditions which ensure the boundednness of maximal operator Mφ: Lp(·)(ℝn) → Lq(·)w (ℝn) are found, when for the pair of Banach function spaces (Lp(·)(ℝn) , Lq(·)(ℝn)) holds weak Minkowski’s inequality.

Keywords: Maximal operator, variable Lp spaces

Kopaliani Tengiz: A Characterization of Some Weighted Norm Inequalities for Maximal Operators. Z. Anal. Anwend. 29 (2010), 401-412. doi: 10.4171/ZAA/1414