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 A_p 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.

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doi:10.5186/aasfm.2015.4042