Cauchy and poisson integrals of ultradistributions in D′(*, L^s)

Abstract

The authors continue their study of Cauchy and Poisson integrals of ultradistributions in D′(*. Ls), which are functions of the complex variable z ∈ TC = Rdbl;n + iC, where C is a regular cone in Rdbl;n. Here, pointwise growth of the Cauchy integral and the boundary value property of the Poisson integral are extended to further values of s for ultradistributions in D′(*, Ls).