On relations between norms in weighted Lebesgue and weighted Hölder spaces for operators with local singularities

Autor:	Anna Tarasenko, Oleksandr Karelin
Rok vydání:	2016
Předmět:	Discrete mathematics Class (set theory) Mathematics::Dynamical Systems Functional analysis General Mathematics Singular integral operators of convolution type Lebesgue's number lemma Operator theory Lebesgue integration Connection (mathematics) symbols.namesake symbols Lp space Mathematics
Zdroj:	Boletín de la Sociedad Matemática Mexicana. 22:503-516
ISSN:	2296-4495 1405-213X
DOI:	10.1007/s40590-016-0118-6
Popis:	The norms in weighted Holder spaces and in weighted Lebesgue spaces are different in their character and any direct connection between the norms of these spaces should not be expected. However, in this work, a special class of operators was found, for which we obtained an inequality that connects the norms of these operators acting on weighted Lebesgue spaces and acting on weighted Holder spaces. A description of such operators and a relation among parameters of these spaces are given. In particular, integral operators with local endpoint singularities belong to the considered class. These results can be used in the study of operators on weighted Holder spaces, based on known results for operators acting on weighted Lebesgue spaces.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4cb56a5afd2031d3561aa45583d4a790 https://doi.org/10.1007/s40590-016-0118-6 Zobrazit plný text záznamu Full text from SpringerLink