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

Seria
Rozprawy Matematyczne tom/nr w serii: 489 wydano: 2013
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EN
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.
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Seria
Rozprawy Matematyczne tom/nr w serii: 489
Liczba stron
114
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
autor
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
autor
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
  • Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
  • Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan
autor
  • Hausdorff Center for Mathematics & Institute for Numerical Simulation, Endenicher Allee 62, 53115 Bonn, Germany
Bibliografia
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm489-0-1
Identyfikatory
DOI
10.4064/dm489-0-1
Kolekcja
DML-PL
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