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

### Volume 161 / 2020

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.