Integrability near the Boundary of the Poisson Integral of Some Singular Measures

【摘要】 We consider the Poisson integral u = P *μ on the half-space R +N+1( N1＞) (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,integral from Rn up(x,y)dx～y-τ( y＞0,τ=(N-s )(p-1)) (Given f＞0 and g＞0,"f～g " will mean that there exist constants C1 and C2,such that C1 f≤g≤C2f).更多还原

【Abstract】 We consider the Poisson integral u = P *μ on the half-space R +N+1( N1＞) (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,integral from Rn up(x,y)dx～y-τ( y＞0,τ=(N-s )(p-1)) (Given f＞0 and g＞0,"f～g " will mean that there exist constants C1 and C2,such that C1 f≤g≤C2f).更多还原