Tb theorems for Triebel-Lizorkin spaces over special spaces of homogeneous type and their applications
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces
Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.