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We study the boundary properties of u(x,y)=Ky∗μ(x), defined on the half-space R∗+×RN by the convolution of an approximate identity Ky(⋅)(y>0) and the Ahlfors–David singular s-measure μ on RN. The Poisson and the Gauss–Weierstrass integral are unified as special cases in our setting. The sharp Lp estimates of the function u(x,y) near the boundary are given. In particular, we show that ∫RNup(x,y)dx∼1δ(y)(N−s)(p−1)as ...
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