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Application of Interpolation Inequalities to the Study of Operators with Linear Fractional Endpoint Singularities in Weighted Hölder Spaces
Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
- 1 Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
- 2 Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
Applied Mathematics·Volume 05 (2014)·Pages 2779–2785·Published 9 October 2014·DOI10.4236/am.2014.517266
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Abstract
In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted H ö lder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted H ö lder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.
KeywordsEndpoint SingularitiesWeighted Holder SpaceWeighted Lebesgue SpacesRelation between NormsBoundedness
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