A Singular Moser-Trudinger Inequality on Metric Measure Space

Abstract

. Let ( X , d , µ ) be a metric space with a Borel-measure µ , suppose µ satisfies the Ahlfors-regular condition, i.e. where b 1 , b 2 are two positive constants and s is the volume growth exponent. In this paper, we mainly study two things, one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2. The other is to study the generalized Moser-Trudinger inequality with a singular weight.