TITLE:
Application of Interpolation Inequalities to the Study of Operators with Linear Fractional Endpoint Singularities in Weighted Hölder Spaces
AUTHORS:
Oleksandr Karelin, Anna Tarasenko
KEYWORDS:
Endpoint Singularities, Weighted Holder Space, Weighted Lebesgue Spaces, Relation between Norms, Boundedness
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.17,
October
23,
2014
ABSTRACT: In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder 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 Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.