Boundary limits for fractional Poisson $a$-extensions of $L^p$ boundary functions in a cone

Lei Qiao and Tao Zhao

Vol. 272 (2014), No. 1, 227–236

DOI: 10.2140/pjm.2014.272.227

Abstract

If one replaces the Poisson kernel of a cone by the Poisson $a$-kernel, then normalized Poisson integrals with respect to the stationary Schrödinger operator converge along approach regions wider than the ordinary nontangential cones. In this paper we present new and simplified proofs of these results. We also generalize the result by Mizuta and Shimomura to the smooth cones.

Keywords

boundary limit, Poisson $a$-integral, stationary Schrödinger operator, cone

Mathematical Subject Classification 2010

Primary: 31B05, 31B10

Milestones

Received: 22 August 2013

Revised: 29 December 2013

Accepted: 25 February 2014

Published: 9 October 2014