A simple characterization of weighted Sobolev spaces with bounded multiplication operator

Sobolev Spaces with Respect to Measures in Curves and Zeros of Sobolev Orthogonal Polynomials

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the unif...

Approximation Theory for Weighted Sobolev Spaces on Curves

In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of ...

The Multiplication Operator in Sobolev Spaces with Respect to Measures

We consider the multiplication operator, M, in Sobolev spaces with respect to general measures and give a characterization for M to be bounded, in terms of sequentially dominated measures. This has important consequences for the asymptotic behaviour of Sobolev orthogonal polynomials. Also, we study properties of Sobolev spaces with respect to measures. 2001 Academic Press

A Note on Weighted Composition Operators on L^p-Spaces

Weighted composition operators between Lipschitz algebras of complex-valued bounded functions

‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.