Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups
arXiv:1506.01208
Abstract
We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev(HLS) inequality based on this representation. The proof rests on a new inequality for a fractional Littlewood-Paley -function.
13 pages