Geodesic
Interpolation of Spaces of Functions of Positive Smoothness on a Domain
Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 98-110

Voir la notice de l'article provenant de la source Math-Net.Ru

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{TRSPY_2021_312_a4,
     author = {O. V. Besov},
     title = {Interpolation of {Spaces} of {Functions} of {Positive} {Smoothness} on a {Domain}},
     journal = {Informatics and Automation},
     pages = {98--110},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a4/}
}
TY  - JOUR
AU  - O. V. Besov
TI  - Interpolation of Spaces of Functions of Positive Smoothness on a Domain
JO  - Informatics and Automation
PY  - 2021
SP  - 98
EP  - 110
VL  - 312
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a4/
LA  - ru
ID  - TRSPY_2021_312_a4
ER  - 
%0 Journal Article
%A O. V. Besov
%T Interpolation of Spaces of Functions of Positive Smoothness on a Domain
%J Informatics and Automation
%D 2021
%P 98-110
%V 312
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a4/
%G ru
%F TRSPY_2021_312_a4
O. V. Besov. Interpolation of Spaces of Functions of Positive Smoothness on a Domain. Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 98-110. http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a4/