Besov-type spaces of variable smoothness on rough domains

Abstract

The paper puts forward new Besov spaces of variable smoothness B As a corollary, an exact description of the traces of 2-microlocal Besov-type spaces and weighted Besov-type spaces on rough domains is obtained.

Dilation in function spaces with general weights

“…Further results such as the ϕ-transform characterization in the sense of Frazier and Jawerth, the case p = ∞, duality, complex interpolation, the smooth atomic, molecular and wavelet decomposition and the characterization of these function spaces in terms of the difference relations are given in [6] and [7]. The above function spaces whose elements are not distributions, but rather functions that are locally integrable in some power are studied by Tyulenev [31], [32] and [33] for the Besov case and by the author [8] for Triebel-Lizorkin case.…”

Triebel-Lizorkin spaces with general weights

“…A. Tyulenev has been introduced in [58], [60] and [59] new family of Besov space of variables smoothness which cover many classes of Besov spaces, where the norm on these spaces was defined with the help of classical differences. Based on this weighted class and [14] we introduce Triebel-Lizorkin spaces of variable smoothness, which defined as follows.…”

Complex interpolation of function spaces with general weights

“…In this direction we present the complex interpolation of function spaces of general weigths, were introduced in [12] and [13], which based on Tyulenev class given in [45], [47] and [46].…”