共查询到20条相似文献,搜索用时 15 毫秒
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O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):56-66
The paper is devoted to constructing and studying spaces of functions of positive smoothness on irregular domains of the n-dimensional Euclidean space. We prove embedding theorems that connect the spaces introduced with the Sobolev and Lebesgue spaces. The formulations of the theorems depend on geometric parameters of the domain of definition of functions. 相似文献
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We compare function spaces of dominating mixed smoothness and spaces of best approximation with respect to hyperbolic crosses. 相似文献
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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
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O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2013,280(1):34-45
We establish asymptotic estimates for the Kolmogorov widths of Sobolev classes W p s (K) in the metric of L q (K) for a power-law peak K ? ? d . These estimates are sharp in the order and coincide with order estimates for the unit cube. 相似文献
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David C. Ullrich 《Arkiv f?r Matematik》1991,29(1-2):323-337
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B. E. Klots 《Mathematical Notes》1977,21(1):12-19
The order of the quantity \(\delta (L) = \mathop {\sup }\limits_{\chi _{_{_{_1 } } } } \mathop {\inf }\limits_{\chi _2 } \parallel \chi _1 - \chi _2 \parallel L_S [0,2 = ]\) as L → ∞ is studied for the classes of periodic functionsx 1εW p n (I), andx 2 εW q m (L). Necessary and sufficient conditions under which the inequality $$\parallel x^{(n)} \parallel _{L_p } \leqslant C\parallel x\parallel _{L_q }^x \parallel x^{(m)} \parallel _{L_s }^\beta $$ with the constant independent of x holds for all periodic functions x(t) with \(\int_0^{2\pi } \chi (l)dl = 0\) andx (m) (t εL s [0, 2π] are found. 相似文献
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David C. Ullrich 《Arkiv f?r Matematik》1991,29(1):323-337
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R. Rubalcaba 《Discrete Mathematics》2009,309(10):3280-3291
The fractional analogues of domination and 2-packing in a graph form an interesting pair of dual linear programmes in that the feasible solutions for both are functions from the vertices of the graph to the unit interval; efficient (fractional) domination is accomplished when one function simultaneously solves both LPs. We investigate some structural properties of the functions thus defined and classify some families of graphs according to how and whether the sets of functions intersect, developing tools that have proven useful in approaching problems in domination theory. 相似文献
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Necessary and sufficient conditions on functions and are found in order for the classes of functions
andH
+k
to coincide (k and r are natural numbers).These results are generalizations of [1–4].Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 785–794, December, 1977.The authors thank V. V. Salaev for his unflagging interest in their work. 相似文献
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Letη be a nondecreasing function on (0, 1] such thatη(t)/t decreases andη(+0)=0. Letf ∈L(I n ) (I≡[0,1]. Set $${\mathcal{N}}_\eta f(x) = \sup \frac{1}{{\left| Q \right|\eta (\left| Q \right|^{1/n} )}} \smallint _Q \left| {f(t) - f(x)} \right|dt,$$ , where the supremum is taken over all cubes containing the pointx. Forη=t α (0<α≤1) this definition was given by A.Calderón. In the paper we prove estimates of the maximal functions ${\mathcal{N}}_\eta f$ , along with some embedding theorems. In particular, we prove the following Sobolev type inequality: if $$1 \leqslant p< q< \infty , \theta \equiv n(1/p - 1/q)< 1, and \eta (t) \leqslant t^\theta \sigma (t),$$ , then $$\parallel {\mathcal{N}}_\sigma {f} {\parallel_{q,p}} \leqslant c \parallel {\mathcal{N}}_\eta {f} {\parallel_p} .$$ . Furthermore, we obtain estimates of ${\mathcal{N}}_\eta f$ in terms of theL p -modulus of continuity off. We find sharp conditions for ${\mathcal{N}}_\eta f$ to belong toL p (I n ) and the Orlicz class?(L), too. 相似文献
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V. Ya. Yanchak 《Mathematical Notes》1970,8(4):718-721
Analogs of theorems of Jensen and Weierstrass are proven for functions of variable smoothness, defined on the real line.Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 443–449, October, 1970.In conclusion I wish to express my gratitude to S. M. Nikol'skii and S. B. Stechkin for their valuable advice concerning this work. 相似文献
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Piotr Niemiec 《Central European Journal of Mathematics》2013,11(7):1304-1316
For a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$ , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$ -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point. 相似文献