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A characterization of multipliers in the Hedberg-Netrusov spaces

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Abstract

We expose a criterion of the membership of a function in the space of pointwise multipliers between the Hedberg-Netrusov spaces. The criterion is stated in terms of a pair of discrete weighted inequalities. Connections of the criterion with the problem of rectifiability of Lipschitz surfaces are established.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. I. Parfenov

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  1. A. I. Parfenov
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Correspondence to A. I. Parfenov.

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Original Russian Text © A. I. Parfenov, 2011, published in Matematicheskie Trudy, 2011, Vol. 14, No. 1, pp. 158–194.

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Parfenov, A.I. A characterization of multipliers in the Hedberg-Netrusov spaces. Sib. Adv. Math. 22, 13–40 (2012). https://doi.org/10.3103/S1055134412010026

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