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Ul’yanov-type inequalities and embeddings between Besov spaces: The case of parameters with limit values. (English) Zbl 1386.46031
Summary: In this paper we obtain some limit cases of inequalities of Ul’yanov-type for modulus of smoothness between Lorentz-Zygmund spaces on \(\mathbb{T}^n\). Corresponding embedding theorems for the Besov spaces are investigated.

MSC:
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
46M35 Abstract interpolation of topological vector spaces
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