Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces

Abstract

Let s∈R and 2≤p≤∞. We prove that the Segal-Bargmann transform B is a bounded operator from fractional Hermite-Sobolev spaces WHs,pRn to fractional Fock-Sobolev spaces FRs,p.