Generalized Morrey Spaces for Non-doubling Measures

Abstract.

In this paper, we define the generalized Morrey spaces on \({\mathbb{R}}^{d}\) with the measure μ non-doubling. After defining the space, we shall investigate the properties of maximal operators, fractional integral operators and the singular integral operators. And we shall allude to the vector-valued extension of these operators.

In writing this paper, the author is supported financially by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.