Ul’yanov-type inequalities and embeddings between Besov spaces: The case of parameters with limit values. (English) Zbl 1386.46031

Domínguez, Oscar

Math. Inequal. Appl. 20, No. 3, 755-772 (2017).

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

Keywords:

modulus of smoothness; \(K\)-functionals; Ul’yanov-type inequalities; generalized Lorentz-Zygmund spaces; Besov spaces; embedding theorems