Interpolation theorem for Nikol’skii-Besov type spaceswith mixed metric

Kuanysh Abdrakhmanovich Bekmaganbetov, K.Ye. Kervenev, Ye. Toleugazy

2020

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DOI 10.31489/2020m4/33-42

Data confidence 70 medium

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Abstract

In this paper we study the interpolation properties of Nikol’skii-Besov spaces with a dominant mixed derivative and mixed metric with respect to anisotropic and complex interpolation methods. An interpolation theorem is proved for a weighted discrete space of vector-valued sequences l^α_q(A). It is shown that the Nikol’skii-Besov space under study is a retract of the space l^α_q(Lp). Based on the above results, interpolation theorems were obtained for Nikol’skii-Besov spaces with the dominant mixed derivative and mixed metric.