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Remark on borderline traces of Besov and Triebel-Lizorkin spaces on noncompact hypersurfaces

Skrzypczak L., Tomasz B.

Commentationes Mathematicae

2013

Vol. 53, No. 2

193--209

We investigate borderline traces of Besov and Triebel-Lizorkin spaces. The function spaces are defined on noncompact Riemannian manifolds with bounded geometry. We described spaces of traces on noncompact submanifolds that are also of bounded geometry.

Approximation numbers of Sobolev embeddings between radial Besov and Sobolev spaces

Skrzypczak L., Tomasz B.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

237-255

We prove asymptotic formulas for the behaviour of approximation numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces of radial distributions.

On consistency of summability methods generated by nonlinear integral operators

Tomasz B.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

197-205

Let r,n be two modulars on L(G), and let W be an abstract set of indices. For nonlinear integral op-erators T(w) and S(w) on L(G), we give sufficient conditions for two methods of summability gen-erated by T(w) and S(w) to be consistent for sequences (f(w)) of functions of L(G), in the sense of modular r.