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In this paper we present a comprehensive treatment of function spaces with logarithmic
smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: Sharp …

In this paper, the authors prove some Franke–Jawerth embedding for the Besov-type spaces
B p, qs, τ (R n) and the Triebel–Lizorkin-type spaces F p, qs, τ (R n). By using some limiting …

We introduce truncated Besov and Triebel–Lizorkin function spaces and study their main
properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to …

We study unboundedness of smoothness Morrey spaces on bounded domains Ω⊂ R n in
terms of growth envelopes. It turns out that in this situation the growth envelope function is …

We generalize here the notion of interpolation space of given exponent by replacing this
exponent with Boyd functions. In particular, this approach leads to the usual interpolation …

The research monograph expounds the foundation of a new theory of parabolic initial-
boundary-value problems in scales of generalized anisotropic Sobolev spaces. These …

We study necessary and sufficient conditions for embeddings of Besov spaces of
generalized smoothness B p, q σ, N (R n) into generalized Hölder spaces Λ∞, r μ (⋅)(R n) …

Optimal embeddings of spaces of generalized smoothness in the critical case Page 1 Optimal
embeddings of spaces of generalized smoothness in the critical case Cornelia Schneider1 …