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Displaying similar documents to “Kernel functions and conformal mapping”

On the angular limits of Bloch functions.

Joan J. Carmona, Julià Cufi, Christian Pommerenke (1988)

Publicacions Matemàtiques

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This paper contains a method to associate to each function f in the little Bloch space another function f* in the Bloch space in such way that f has a finite angular limit where f* is radially bounded. The idea of the method comes from the theory of lacunary series. An application to conformal mapping from the unit disc to asymptotically Jordan domains is given.

Intrinsic characterizations of distribution spaces on domains

V. Rychkov (1998)

Studia Mathematica

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We give characterizations of Besov and Triebel-Lizorkin spaces B p q s ( Ω ) and F p q s ( Ω ) in smooth domains Ω ⊂ ℝ n via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.