In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale.

Let f be an analytic function mapping the unit disk D into itself. We give necessary and sufficient conditions on the local behavior of f near a finite set of boundary points that require f to be a finite Blaschke product.

For positive semi-definite tensors like diffusion tensors in the plane it is possible to calculate several different means or p-averages. These are related to p-norms for functions, but produce mappings rather than numbers as means. We compare these means for various values of the real parameter p. One important future application is the filtering and interpolation of tensor fields in Diffusion...

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derivations, equational logic and interpolation Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation property.

In this note we study some basic properties of the γinterpolation method introduced in [6] e.g. interpolation of Bochner spaces and interpolation of analytic operator valued functions in the sense of Stein. As applications we consider the interpolation of almost summing operators (in particular γ-radonifying and Hilbert-Schmidt operators) and of γ-Sobolev spaces as introduced in [6]. We also co...