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On Weighted Norms of Riesz Transforms Equal to One

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Abstract

We consider the vector Riesz transform ∇tΔ-(t+s)/2 divs of even order s + t in the weighted space L 2(ℝn;|x|a). We establish that for t ≠ s, n >3 its norm is equal to one on some interval of values of a, while inside the interval a stronger estimate for a subordinate norm is valid.

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  1. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk

    E. A. Kalita

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  1. E. A. Kalita
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Kalita, E.A. On Weighted Norms of Riesz Transforms Equal to One. Mathematical Notes 72, 799–810 (2002). https://doi.org/10.1023/A:1021437929109

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