Abstract
Interpolation spaces are described for spaces of functions of positive smoothness on a domain \(G\) of the Euclidean space \(\mathbb R^n\) that satisfies the flexible cone condition. As a consequence, multiplicative estimates for the norms of functions are obtained. The arguments are based on integral representations of functions over a flexible cone in terms of the local approximations of functions by polynomials and on estimates of the arising convolution operators.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 312, pp. 98–110 https://doi.org/10.4213/tm4127.
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Besov, O.V. Interpolation of Spaces of Functions of Positive Smoothness on a Domain. Proc. Steklov Inst. Math. 312, 91–103 (2021). https://doi.org/10.1134/S0081543821010053
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DOI: https://doi.org/10.1134/S0081543821010053