Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 773-791

TWO-WEIGHT NORM INEQUALITIES ON MORREY SPACES

Hitoshi Tanaka

The University of Tokyo, Graduate School of Mathematical Sciences
Tokyo, 153-8914, Japan; htanaka 'at' ms.u-tokyo.ac.jp

Abstract. A description of all the admissible weights similar to the Muckenhoupt class Ap is an open problem for the weighted Morrey spaces. In this paper necessary condition and sufficient condition for two-weight norm inequalities on Morrey spaces to hold are separately given for the Hardy-Littlewood maximal operator. Necessary and sufficient condition is also verified for the power weights.

2010 Mathematics Subject Classification: Primary 42B25, 42B35.

Key words: Hardy-Littlewood maximal operator, Hausdorff content, Morrey space, Muckenhoupt weight class, one and two weight norm inequality.

Reference to this article: H. Tanaka: Two-weight norm inequalities on Morrey spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 773-791.

Full document as PDF file

doi:10.5186/aasfm.2015.4042

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