Boundary limits for fractional Poisson<i>a</i>-extensions of<i>L</i><sup><i>p</i></sup>boundary functions in a cone

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If one replaces the Poisson kernel of a cone by the Poisson a-kernel, then normalized Poisson integrals with respect to the stationary Schrodinger 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.

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