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Brushlet characterization of the Hardy space H1(R) and the space BMO.

Lasse Borup (2005)

Collectanea Mathematica

A typical wavelet system constitutes an unconditional basis for various function spaces -Lebesgue, Besov, Triebel-Lizorkin, Hardy, BMO. One of the main reasons is the frequency localization of an element from such a basis. In this paper we study a wavelet-type system, called a brushlet system. In [3] it was noticed that brushlets constitute unconditional bases for classical function spaces such as the Triebel-Lizorkin and Besov spaces. In this paper we study brushlet expansions of functions in the...

C 1 -smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

Irina Kmit (2011)

Commentationes Mathematicae Universitatis Carolinae

We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the C 1 -continuity property of these operators over Sobolev-type spaces of periodic functions.

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