Geodesic
Interpolation of Spaces of Functions of Positive Smoothness on a Domain
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 98-110

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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.
Keywords: regular domain, spaces of functions of positive smoothness
Mots-clés : interpolation, multiplicative estimates. 
@article{TM_2021_312_a4,
     author = {O. V. Besov},
     title = {Interpolation of {Spaces} of {Functions} of {Positive} {Smoothness} on a {Domain}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {98--110},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_312_a4/}
}
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O. V. Besov. Interpolation of Spaces of Functions of Positive Smoothness on a Domain. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 98-110. http://geodesic.mathdoc.fr/item/TM_2021_312_a4/