Abstract
By taking an interest in a natural extension to the small parameters of the trace inequality for Morrey spaces, Orlicz–Morrey spaces are introduced and some inequalities for generalized fractional integral operators on Orlicz–Morrey spaces are established. The local boundedness property of the Orlicz maximal operators is investigated and some Morrey-norm equivalences are also verified. The result obtained here sharpens the one in our earlier papers.
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The first author was supported by Grant-in-Aid for Young Scientists (B) (No. 21740104) Japan Society for the Promotion of Science. The third author is supported by the Global COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and was supported by Fūjyukai foundation.
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Sawano, Y., Sugano, S. & Tanaka, H. Orlicz–Morrey Spaces and Fractional Operators. Potential Anal 36, 517–556 (2012). https://doi.org/10.1007/s11118-011-9239-8
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DOI: https://doi.org/10.1007/s11118-011-9239-8
Keywords
- Orlicz–Morrey space
- Generalized fractional integral operator
- Generalized fractional maximal operator
- Orlicz maximal operator
- Trace inequality
- Olsen’s inequality
- Wiener–Stein equivalence