锥中边界函数分式Poisson展式的边界极限

Boundary Limits for Fractional Poisson Extensions of Boundary Functions in a Cone

设GC_((n))(Ω)为有界开集,f∈L(C_((n))(Ω)),PIΩf(P)=∫s_(((n)(Ω)))(P,Q)f(Q)dσQ,其中PI_((Ω))(P,Q)是锥C_((n))(Ω)内的Poisson核.本文将给出正规化算子(PIΩf(P))/(PIΩXG(P))在锥中的边界极限,所得结果推广了潘国双在半空间中的相关结论.

Let G be a bounded open set in δCn（Ω）, f∈L（δCn（Ω）） and PIΩf（P）=∫Sn（Ω）PIΩ（P,Q）f（Q）dσQ, where PIΩ（P,Q） is the Poisson kernel in a cone Cn（Ω）. In this paper we shall consider the boundary limits of the normalized operator PIΩf（P）/PIΩXG（P） in a cone, which generalizes the result obtained by Pan in a half space.