A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces

Yiyu Liang, et al. A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces. 2013. <http://eudml.org/doc/285953>.

@book{YiyuLiang2013,
abstract = {In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is an application of the Peetre maximal function. This idea originates from recent findings in the abstract coorbit space theory obtained by Holger Rauhut and Tino Ullrich. In this new setting, the authors establish the boundedness of pseudo-differential operators based on atomic and molecular characterizations and also the boundedness of Fourier multipliers. Characterizations of these function spaces by means of differences and oscillations are also established. As further applications of this new framework, the authors reexamine and polish some existing results for many different scales of function spaces.},
author = {Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich},
keywords = {Besov spaces; Triebel-Lizorkin spaces; atoms; molecules; differences; oscillations; wavelets; embeddings; multipliers; pseudo-differential operators},
language = {eng},
title = {A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces},
url = {http://eudml.org/doc/285953},
year = {2013},
}

TY - BOOK
AU - Yiyu Liang
AU - Dachun Yang
AU - Wen Yuan
AU - Yoshihiro Sawano
AU - Tino Ullrich
TI - A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces
PY - 2013
AB - In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is an application of the Peetre maximal function. This idea originates from recent findings in the abstract coorbit space theory obtained by Holger Rauhut and Tino Ullrich. In this new setting, the authors establish the boundedness of pseudo-differential operators based on atomic and molecular characterizations and also the boundedness of Fourier multipliers. Characterizations of these function spaces by means of differences and oscillations are also established. As further applications of this new framework, the authors reexamine and polish some existing results for many different scales of function spaces.
LA - eng
KW - Besov spaces; Triebel-Lizorkin spaces; atoms; molecules; differences; oscillations; wavelets; embeddings; multipliers; pseudo-differential operators
UR - http://eudml.org/doc/285953
ER -