Abstract
The mapping properties of the Cauchy singular integral operator with
constant coefficients are studied in couples of spaces equipped with
weighted uniform norms. Recently weighted Besov type spaces got more and
more interest in approximation theory and, in particular, in the numerical
analysis of polynomial approximation methods for Cauchy singular integral
equations on an interval. In a scale of pairs of weighted Besov spaces the
authors state the boundedness and the invertibility of the Cauchy singular
integral operator. Such result was not expected for a long time and it will
affect further investigations essentially. The technique of the paper is
based on properties of the de la Vallee Poussin operator constructed with
respect to some Jacobi polynomials.
Anno
2002
Autori IAC
Tipo pubblicazione
Altri Autori
Mastroianni G., Russo M.G., Themistoclakis W.
Editore
Birkhäuser,
Rivista
Integral equations and operator theory