Abstract
We establish some reiteration theorems for limiting K-interpolation methods, thereby obtaining new limiting variants of the classical reiteration theorem. An application to the Fourier transform is given.
Highlights
Let (A0, A1) be a compatible couple of quasi-normed spaces, that is, we assume that both A0 and A1 are continuously embedded in the same Hausdorff topological vector space
The classical K -interpolation space Aθ,q = (A0, A1)θ,q is formed by all those f ∈ A0 + A1 for which the quasi-norm f Aθ,q =
Let b be a slowly varying function, the K -interpolation space Aθ,q;b = (A0, A1)θ,q;b consists of those f ∈ A0 + A1 for which the quasi-norm f Aθ,q;b =
Summary
Let (A0, A1) be a compatible couple of quasi-normed spaces, that is, we assume that both A0 and A1 are continuously embedded in the same Hausdorff topological vector space. Let b be a slowly varying function (see, for instance, [5]), the K -interpolation space Aθ,q;b = (A0, A1)θ,q;b consists of those f ∈ A0 + A1 for which the quasi-norm f Aθ,q;b = See [5,6,7] for different reiteration theorems for this extended scale in limiting cases.
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