Czechoslovak Mathematical Journal

, Volume 64, Issue 1, pp 209–228 | Cite as

Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces

Article

Abstract

Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev’s inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger’s inequality and the continuity for Riesz potentials.

Keywords

grand Morrey space variable exponent non-doubling measure metric measure space Riesz potential maximal operator Sobolev’s inequality Trudinger’s exponential inequality continuity 

MSC 2010

31B15 46E35 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.Faculty of Education and Welfare ScienceOita UniversityDannoharu Oita-CityJapan
  2. 2.Department of Mathematics, Graduate School of EducationHiroshima UniversityHigashi-HiroshimaJapan

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