The following space will be useful because of its geometric interpretation:Namely, by a theorem of Smirnov and Riesz, a univalent map F of D onto a simply connected domain W will belong to Lð1; 1Þ if and only if the boundary curve qW is rectifiable ([D1], Theorem 3.12). The result is often formulated in the literature only for Jordan domains W, but a compactness and covering argument allows us to extend it easily to ar-Donaire, Girela and Vukotić, Möbius invariant spaces 44 Brought to you by |
This paper is a continuation of our earlier work and focuses on the structural and geometric properties of functions in analytic Besov spaces, primarily on univalent functions in such spaces and their image domains. We improve several earlier results.
We study differentiability properties of Zygmund functions and series of Weierstrass type in higher dimensions. While such functions may be nowhere differentiable, we show that, under appropriate assumptions, the set of points where the incremental quotients are bounded has maximal Hausdorff dimension.
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