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Duduchava, R.V. (1963) Unidimensional Singular Integral Operator Algebras in Spaces of Holder Functions with Weight. Proceedings of A. Razmadze Mathematical Institute, 43, 19-52. (in Russian)

has been cited by the following article:

• 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.