JournalszaaVol. 29, No. 4pp. 401–412

A Characterization of Some Weighted Norm Inequalities for Maximal Operators

  • Tengiz Kopaliani

    Tbilisi State University, Georgia
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Abstract

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

Cite this article

Tengiz Kopaliani, A Characterization of Some Weighted Norm Inequalities for Maximal Operators. Z. Anal. Anwend. 29 (2010), no. 4, pp. 401–412

DOI 10.4171/ZAA/1414