Lipschitz Spaces and Fractional Integral Operators Associated with Nonhomogeneous Metric Measure Spaces

Abstract

The fractional operator on nonhomogeneous metric measure spaces is introduced, which is a bounded operator from $L^p\left(\mu \right)$ into the space $L^{q,\infty }\left(\mu \right)$. Moreover, the Lipschitz spaces on nonhomogeneous metric measure spaces are also introduced, which contain the classical Lipschitz spaces. The authors establish some equivalent characterizations for the Lipschitz spaces, and some results of the boundedness of fractional operator in Lipschitz spaces are also presented.