Abstract and Applied Analysis (Jan 2014)
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 Lpμ into the space Lq,∞μ. 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.