Embeddings of anisotropic Besov spaces into Sobolev spaces

Optimal Domain Spaces in Orlicz-sobolev Embeddings

We deal with Orlicz-Sobolev embeddings in open subsets of R. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given Orlicz space. Moreover, the optimal Orlicz-Sobolev space is exhibited whenever it exists. Parallel questions are addressed for Orlicz-Sobolev embeddings into Orlicz spaces ...

Optimal Sobolev embeddings and Function Spaces

Univalent Interpolation in Besov Spaces and Superposition into Bergman Spaces

We characterize the superposition operators from an analytic Besov space or the little Bloch space into a Bergman space in terms of the order and type of the symbol. We also determine when these operators are continuous or bounded. Along the way, we prove new non-centered Trudinger-Moser inequalities and solve the problem of interpolation by univalent functions in analytic Besov spaces. Introdu...

Entropy numbers of embeddings of some 2-microlocal Besov spaces

We investigate compactness and asymptotic behaviour of the entropy numbers of embeddings B s1,s1 p1,q1 (R, U) ↪→ B s2,s2 p2,q2 (R, U) . Here B ′ p,q (Rn, U) denotes a 2-microlocal Besov space with a weight given by the distance to a fixed set U ⊂ Rn.

Widths of embeddings of 2-microlocal Besov spaces

We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a d-set U ⊂ R. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.