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Approximation spaces, limiting interpolation and Besov spaces. (English) Zbl 1326.46020
Summary: With the help of limiting interpolation we determine the spaces obtained by iteration of approximation constructions. Then we apply the reiteration formula and limiting interpolation to investigate several problems on Besov spaces, including embeddings in Lorentz-Zygmund spaces and distribution of Fourier coefficients.

MSC:
46B70 Interpolation between normed linear spaces
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
46M35 Abstract interpolation of topological vector spaces
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