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Weighted norm inequalities involving gradients
Published online by Cambridge University Press: 14 November 2011
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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