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On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  03 April 2020

Ritva Hurri-Syrjänen ,
Takao Ohno  and
Tetsu Shimomura
Ritva Hurri-Syrjänen
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, FI-00014Helsinki, Finland e-mail: ritva.hurri-syrjanen@helsinki
Takao Ohno
Affiliation:
Faculty of Education, Oita University, Dannoharu Oita-city870-1192, Japan e-mail: t-ohno@oita-u.ac.jp
Tetsu Shimomura*
Affiliation:
Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima739-8524, Japan
*
e-mail: tshimo@hiroshima-u.ac.jp
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Abstract

We give Trudinger-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric measure spaces. Our results are new even for the doubling metric measure setting. In particular, our results improve and extend the previous results in Morrey spaces of an integral form in the Euclidean case.

Keywords

Riesz potentialTrudinger’s inequalityOrlicz-Morrey spacesmetric measure spacenon-doubling measure

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Secondary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 75 - 90
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

R. Hurri-Syrjänen’s visit to Hiroshima University was supported by her grant from the Academy of Finland.

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