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Weighted norm inequalities involving gradients

  • C. Carton-Lebrun (a1) and H. P. Heinig (a2)

Synopsis

Let then, for certain weight functions u and v and indices p,q, it is shown that ∥Tαfq, uC∥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.

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