Boundary Limits for Fractional Poisson Extensions of Boundary Functions in a Cone
Qiao Le · Advances in Mathematics · 2014
Let G be a bounded open set in C_n(Ω),f∈L(C_n(Ω)) and PIΩf(P)=∫S_n(Ω) PI_Ω(P,Q)f(Q)dσ_Q,where PI_Ω(P,Q) is the Poisson kernel in a cone C_n(Ω).In this paper we shall consider the boundary limits of the normalized operator PI_Ωf(P)/PI_ΩXG(P) in a cone,which generalizes the result obtained by Pan in a half space.