Petr Gurka

Sharpness of embeddings in logarithmic Bessel-potential spaces

This paper is a continuation of [ 4 ], where embeddings of certain logarithmic Bessel-potential spaces (modelled upon generalised Lorentz-Zygmund spaces) in appropriate Orlicz spaces (with Young functions of single and double exponential type) were derived. The aim of this paper is to show that these embedding results are sharp in the sense of [ 8 ].

Concentration-Compactness Principle for Generalized Trudinger Inequalities

Let Ω ⊂ R, n ≥ 2, be a bounded domain and let α < n−1. We prove the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space W 1 0 L n log L(Ω) into the Orlicz space with the Young function exp (

Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces

In our recent paper [Compact and continuous embeddings of logarithmic Bessel potential spaces. Studia Math. 168 (2005), 229 – 250] we have proved an embedding of a logarithmic Bessel potential space with order of smoothness σ less than one into a space of λ(·)-Hölder-continuous functions. We show that such an embedding is not compact and that it is sharp.

Decay of (p,q)-Fourier coefficients.

We show that essentially the speed of decay of the Fourier sine coefficients of a function in a Lebesgue space is comparable to that of the corresponding coefficients with respect to the basis formed by the generalized sine functions sinp,q.

Nuclearity and non-nuclearity of some Sobolev embeddings on domains

Necessary and sufficient conditions are given for certain embeddings of Sobolev type on domains to be nuclear.