Application of integral representations of functions to interpolation of spaces of differentiable functions and Fourier multipliers (Q5899935)

Let G be domain in \({\mathbb{R}}^ n\) satisfying some anisotropic cone conditions. Let \(s=(s_ 1,...,s_ n)>0\), \(1\leq p<\infty\), \(1\leq q<\infty\), then \(B^ s_{pq}(G)\) are the usual anisotropic Besov spaces. The main aim of the paper is twofold. First the author proves real and complex interpolation theorems for the spaces \(B^ s_{pq}(G)\). Secondly, rather sharp Fourier multiplier theorems for \(L_ p\)-spaces are proved, extending earlier results. All assertions are based on a sophisticated technique of integral representations of functions.