# A Characterization of Some Weighted Norm Inequalities for Maximal Operators

### Tengiz Kopaliani

Tbilisi State University, Georgia

## 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