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Trace inequalities for weighted Hardy—Sobolev spaces in the non-diagonal case

Published online by Cambridge University Press:  21 March 2012

Carme Cascante  and
Joaquin M. Ortega
Carme Cascante
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain (cascante@ub.edu; ortega@ub.edu)
Joaquin M. Ortega
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain (cascante@ub.edu; ortega@ub.edu)
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Abstract

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We give characterizations of the positive Borel measures μ on so that the weighted Hardy–Sobolev spaces are imbedded in Lq(dμ), for a range of s > 0, 0 < p, q < + ∞, q ≠ p, where w is a doubling weight in the unit sphere of ℂn.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 2 , April 2012 , pp. 329 - 357
Copyright
Copyright © Royal Society of Edinburgh 2012