Weighted Sobolev spaces on curves

Authors:
Venancio Alvarez;Domingo Pestana;José M. Rodríguez;Elena Romera
Affiliations:
Departamento de Análisis Matemático, Facultad de Ciencias, Campus de Teatinos, 29071 Málaga, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30 28911 Leganés, Madrid, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30 28911 Leganés, Madrid, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30 28911 Leganés, Madrid, Spain
Venue:
Journal of Approximation Theory
Year:
2002

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Abstract

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