Sobolev's Inequality for Riesz Potentials of Functions in Musielak-Orlicz-Morrey Spaces Over Non-doubling Metric Measure Spaces

摘要

Our aim in this paper is to establish a generalization of Sobolev's inequality for Riesz potentials I(alpha(.),tau)f of order alpha(.) with f is an element of L-Phi,L-k,L-theta(X) over bounded non-doubling metric measure spaces. As a corollary we obtain Sobolev's inequality for double phase functionals with variable exponents.