Abstract

We work with Triebel–Lizorkin spaces \(F_{q}^{s}L_{p,r}({\mathbb {R}}^{n})\) and Besov spaces \(B_{q}^{s} L_{p,r}({\mathbb {R}}^{n})\) with Lorentz smoothness. Using their characterizations by real interpolation we show how to transfer a number of properties of the usual Triebel–Lizorkin and Besov spaces to the spaces with Lorentz smoothness. In particular, we give results on diffeomorphisms, extension operators, multipliers and we also show sufficient conditions on parameters for \(F_{q}^{s}L_{p,r}({\mathbb {R}}^{n})\) and \(B_{q}^{s}L_{p,r}({\mathbb {R}}^{n})\) to be multiplication algebras.

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