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1.
O. V. Besov 《Mathematical Notes》1996,64(3):303-315
We obtain sufficient conditions on a domainG ? ?n for functions defined onG to be extendable by zero to the entire space ?n with smoothness preserved in an integral norm. 相似文献
2.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
3.
4.
Doklady Mathematics - For spaces of functions of positive smoothness defined on irregular domains of n-dimensional Euclidean space, an embedding theorem into spaces of the same type is proved and... 相似文献
5.
6.
Doklady Mathematics - An interpolation theorem for spaces of functions of positive smoothness on a domain with flexible cone condition is established. 相似文献
7.
O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):25-45
On an irregular domain G ⊂ ℝ
n
of a certain type, we introduce spaces of functions of fractional smoothness s > 0. We prove embedding theorems relating these spaces to the Sobolev spaces W
p
m
(G) and Lebesgue spaces L
p
(G). 相似文献
8.
K. O. Besov 《Mathematical Notes》1998,64(4):450-460
We consider the following representation of polyharmonic functions on the unit ballD
m
: 450-1 where the
j
are harmonic onD
m
. We study the relation between uniform boundary properties ofƒ (its smoothness and growth while approaching the boundary) and the same properties of the terms in this representation. The theorems proved in this paper generalize some results obtained by Dolzhenko in the theory of polyanalytic functions.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 518–530, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01366. 相似文献
9.
O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):25-36
On an irregular domain G ⊂ ℝ
n
of a certain type, we introduce function spaces of fractional smoothness s > 0 that are similar to the Lizorkin-Triebel spaces. We prove embedding theorems that show how these spaces are related to
the Sobolev and Lebesgue spaces W
p
m
(G) and L
p
(G).
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 260, pp. 32–43. 相似文献
10.
O. V. Besov 《Mathematical Notes》1998,64(3):303-315
We obtain sufficient conditions on a domainG ⊂ ℝn for functions defined onG to be extendable by zero to the entire space ℝn with smoothness preserved in an integral norm.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 351–365, September, 1998.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00243 and by program “Leading
Science Schools” under grant No. 96-15-96102. 相似文献