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Gagliardo--Nirenberg inequality for generalized Riesz potentials of functions in Musielak--Orlicz spaces over quasi-metric measure spaces

Volume 161 / 2020

Daiki Hashimoto, Yoshihiro Sawano, Tetsu Shimomura Colloquium Mathematicum 161 (2020), 51-66 MSC: Primary 46E35; Secondary 46E30. DOI: 10.4064/cm7535-4-2019 Published online: 24 February 2020

Abstract

Our aim in this paper is to give a Gagliardo–Nirenberg inequality for generalized Riesz potentials $I_{\rho , \mu , \kappa }f$ of functions in Musielak–Orlicz spaces over quasi-metric measure spaces, as an extension of work of Mizuta et al. (2012). What is new in this paper is that $\rho $ depends on $x \in X$ and that the underlying measure $\mu $ is not doubling.

Authors

  • Daiki HashimotoNagasakihokuyodai High School
    Nagasaki 851-2127, Japan
    e-mail
  • Yoshihiro SawanoDepartment of Mathematics
    and Information Sciences
    Tokyo Metropolitan University
    1-1 Minami-Ohsawa, Hachioji, 192-0397, Japan
    e-mail
  • Tetsu ShimomuraDepartment of Mathematics
    Graduate School of Education
    Hiroshima University
    Higashi-Hiroshima 739-8524, Japan
    e-mail

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