Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

Approximation and entropy numbers in Besov spaces of generalized smoothness

Let X and Y be Banach (or quasi-Banach) spaces and let T ∈ L(X,Y ) be a compact operator. In order to measure “the degree of compactness of T” one can use the asymptotic decay of the sequence of approximation numbers of T or the decay of the sequence of entropy numbers of T. In general, the behaviour of these sequences is quite different. However, as we shall show, under certain assumptions the...

Local Growth Envelopes of Besov Spaces of Generalized Smoothness

The concept of local growth envelope (ELGA, u) of the quasi-normed function space A is applied to the Besov spaces of generalized smoothness B p,q (Rn).

Sharp Embeddings of Besov Spaces with Logarithmic Smoothness

We prove sharp embeddings of Besov spaces B p,r (R ) with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79–92) they have written: “Nevertheless a direct proof, avoiding the machinery of function spaces, would be...

Generalized Lebesgue Spaces and Application to Statistics

Statistics requires consideration of the “ideal estimates” defined through the posterior mean of fractional powers of finite measures. In this paper we study L1= , the linear space spanned by th power of finite measures, 2 (0; 1). It is shown that L1= generalizes the Lebesgue function space L1= ( ), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach s...

Pointwise Multipliers of Besov Spaces of Smoothness Zero and Spaces of Continuous Functions