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Maximal and Riesz Potential Operators on Musielak–Orlicz Spaces Over Metric Measure Spaces

  • Takao Ohno
  • Tetsu Shimomura
Article
  • 32 Downloads

Abstract

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator \(M_{\lambda }\) on Musielak–Orlicz spaces \(L^{\Phi }(X)\) over bounded metric measure spaces. As an application of the boundedness of \(M_{\lambda }\), we establish a generalization of Sobolev’s inequality for Riesz potentials \(I_{\alpha (\cdot ),\tau }f\) with \(f \in L^{\Phi }(X)\).

Keywords

Maximal functions Riesz potentials Musielak–Orlicz spaces Sobolev’s inequality Metric measure space Lower Ahlfors regular 

Mathematics Subject Classification

Primary 46E35 Secondary 46E30 

Notes

Acknowledgements

We would like to express our thanks to the referees for their kind comments and helpful suggestions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of EducationOita UniversityOita-CityJapan
  2. 2.Department of Mathematics Graduate School of EducationHiroshima UniversityHigashi-HiroshimaJapan

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