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Weighted norm inequalities involving gradients

Published online by Cambridge University Press:  14 November 2011

C. Carton-Lebrun  and
H. P. Heinig
C. Carton-Lebrun
Affiliation:
Department of Mathematics, University of Mons, 7000 Mons, Belgium
H. P. Heinig
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
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Synopsis

Let then, for certain weight functions u and v and indices p,q, it is shown that ∥Tαf∥q, u≦C∥grad f ∥p, v'q > n / α holds. For α=l,p=q and u = v ≡ l this reduces to a result of M. Weiss. In addition we establish n-dimensional weighted Hardy—Littlewood type inequalities ofthe form for large classes of weights.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 331 - 341
Copyright
Copyright © Royal Society of Edinburgh 1989

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