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The problem of traces for sobolev spaces with Muckenhoupt-type weights

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Abstract

An exact description of traces of functions from the weighted Sobolev spaceW l p (Q, γ) on the square are presented in detail. The weight function γ ∈ A p ((0, 1)) depends on one “longitudinal” coordinate x. Traces are characterized in terms of the weighted Besov-type spaces \(\tilde B_p^{l - 1/p}\) ((0, 1), γ) constructed in the paper. The characterization of traces is also obtained in the case p = 1.

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  1. Moscow Institute of Physics and Technology, Moscow, Russia

    A. I. Tyulenev

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  1. A. I. Tyulenev
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Correspondence to A. I. Tyulenev.

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Original Russian Text © A. I. Tyulenev, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 5, pp. 720–732.

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Tyulenev, A.I. The problem of traces for sobolev spaces with Muckenhoupt-type weights. Math Notes 94, 668–680 (2013). https://doi.org/10.1134/S0001434613110084

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  • DOI: https://doi.org/10.1134/S0001434613110084

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