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Sobolev spaces with respect to measures in curves and zeros of Sobolev orthogonal polynomials. (English) Zbl 1169.41002

The authors obtain some criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence, the weighted Sobolev spaces with a bounded multiplication operator are characterized for a large class of weights.

MSC:

41A10 Approximation by polynomials
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46G10 Vector-valued measures and integration
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