Fractional calculus on parabolic Bergman spaces

Abstract

The parabolic Bergman space is the set of all $L^p$-solutions of the parabolic operator $L^{(\alpha)}$. In this paper, we study fractional calculus on parabolic Bergman spaces. In particular, we investigate properties of fractional derivatives of the fundamental solution of the parabolic operator. We show the reproducing property of fractional derivatives of the fundamental solution.