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On convergence for the square root of the Poisson kernel in symmetric spaces of rank 1

Jan-Olav Rönning — 1997

Studia Mathematica

Let P(z,β) be the Poisson kernel in the unit disk , and let P λ f ( z ) = ʃ P ( z , φ ) 1 / 2 + λ f ( φ ) d φ be the λ -Poisson integral of f, where f L p ( ) . We let P λ f be the normalization P λ f / P λ 1 . If λ >0, we know that the best (regular) regions where P λ f converges to f for a.a. points on ∂ are of nontangential type. If λ =0 the situation is different. In a previous paper, we proved a result concerning the convergence of P 0 f toward f in an L p weakly tangential region, if f L p ( ) and p > 1. In the present paper we will extend the result to symmetric spaces X of...

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