Zeitschrift für Analysis und ihre Anwendungen


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Volume 36, Issue 2, 2017, pp. 159–190
DOI: 10.4171/ZAA/1584

Published online: 2017-03-29

Boundedness of the Generalized Fractional Integral Operators on Generalized Morrey Spaces over Metric Measure Spaces

Yoshihiro Sawano[1] and Tetsu Shimomura[2]

(1) Tokyo Metropolitan University, Japan
(2) Hiroshima University, Japan

Our aim in this paper is to deal with the boundedness of the generalized fractional integral operators on generalized Morrey spaces $L_{p,\phi;2}(X;\mu)$ over metric measure spaces. We also discuss a necessary condition for the boundedness of the generalized fractional integral operators. As applications, we establish new results for the predual spaces.

Keywords: Sobolev's inequality, Morrey space, Riesz potential, non-doubling measure, predual spaces

Sawano Yoshihiro, Shimomura Tetsu: Boundedness of the Generalized Fractional Integral Operators on Generalized Morrey Spaces over Metric Measure Spaces. Z. Anal. Anwend. 36 (2017), 159-190. doi: 10.4171/ZAA/1584