Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 264, Issue 12, Pages 2676-2703Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2013.03.012
Keywords
Besov spaces; Triebel-Lizorkin spaces; Generalized smoothness; Regular distributions; Standardization; Atomic decompositions; Fourier series
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Funding
- FEDER funds through COMPETE - Operational Programme Factors of Competitiveness (Programa Operacional Factores de Competitividade)
- Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro)
- Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia) [PEst-C/MAT/UI4106/2011, FCOMP-01-0124-FEDER-022690]
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We establish conditions on the parameters which are both necessary and sufficient in order that Besov and Triebel-Lizorkin spaces of generalized smoothness contain only regular distributions. We also connect this with the possibility of embedding such spaces in some particular Lebesgue spaces. (C) 2013 Elsevier Inc. All rights reserved.
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