Integrability near the boundary of the Poisson integral of some singular measures

We consider the Poisson integral u = P* μ on the half-space R ₊ ^N+1 (N > 1) (or on the unit ball of the complex plane) of some singular measure μ. If μ is an s-measure (0 < s < N), then some sharp estimates of the integration of the harmonic function u near the boundary are given. In particular, we show that for p > 1, (y > 0,τ = (N − s(p−1)) (Given f > 0 and g > 0, “f ∼ g” will mean that there exist constants C ₁ and C ₂ such that C ₁ f ⩽ g ⩽ C ₂ f). Biography: SU Xiaofang(1980–), female, Ph.D. candidate, research direction: fractal and harmonic analysis.