共查询到20条相似文献,搜索用时 31 毫秒
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V. G. Maz'ya 《Journal of Mathematical Sciences》1983,22(6):1851-1855
By definition, the domain Ω ??n belongs to the class EW p l if there exists a continuous linear extension operator . An example is given of a domain Ω ??2 with compact closure and Jordan boundary, having the following properties: (1) The curve ?Ω is not a quasicircle, has finite length and is Lipschitz in a neighborhood of any of its points except one. (2) Ω ε EW p 1 for p<2. and Ω ? EW p 1 for p?2. (3) for p>2 and for p?2. 相似文献
3.
V. G. Maz'ya 《Journal of Mathematical Sciences》1983,23(1):1997-2003
It is proved that for all fractionall the integral \(\int\limits_0^\infty {(p,\ell ) - cap(M_t )} dt^p\) is majorized by the P-th power norm of the functionu in the space ? p l (Rn) (here Mt={x∶¦u(x)¦?t} and (p,l)-cap(e) is the (p,l)-capacity of the compactum e?Rn). Similar results are obtained for the spaces W p l (Rn) and the spaces of M. Riesz and Bessel potentials. One considers consequences regarding imbedding theorems of “fractional” spaces in ?q(dμ), whereμ is a nonnegative measure in Rn. One considers specially the case p=1. 相似文献
4.
In this paper,we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional M2p of a submanifold M n in a general Riemannian manifold N n+m for p = 0,1,...,[n 2 ].As an example,we prove that closed complex submanifolds in complex projective spaces are critical points of the functional M2p,called relatively 2p-minimal submanifolds,for all p.At last,we discuss the relations between relatively 2p-minimal submanifolds and austere submanifolds in real space forms,as well as a special variational problem. 相似文献
5.
The conjecture that every Banach space contains uniformly complementedl p n ’s for some 1≦p≦∞ is verified for subspaces of Banach lattices which do not containl ∞ n ’s uniformly. 相似文献
6.
Andreas M. Hinz Sandi Klavžar Sara Sabrina Zemljič 《Central European Journal of Mathematics》2013,11(6):1153-1157
Hanoi graphs H p n model the Tower of Hanoi game with p pegs and n discs. Sierpinski graphs S p n arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that S p n embeds as a spanning subgraph into H p n if and only if p is odd or, trivially, if n = 1. 相似文献
7.
T. I. Krasnova 《Moscow University Mathematics Bulletin》2012,67(3):133-135
The asymptotics L k ? (f 2 n ) ?? n min{k+1, p} is obtained for the sequence of Boolean functions $f_2^n \left( {x_1 , \ldots ,x_n } \right) = \mathop \vee \limits_{1 \leqslant i < j \leqslant n}$ for any fixed k, p ?? 1 and growing n, here L k ? (f 2 n ) is the inversion complexity of realization of the function f 2 n by k-self-correcting circuits of functional elements in the basis B = {&, ?}, p is the weight of a reliable invertor. 相似文献
8.
A. I. Tyulenev 《Proceedings of the Steklov Institute of Mathematics》2014,284(1):280-295
We characterize the trace of the Sobolev space W p l (? n , γ) with 1 < p < ∞ and weight γ ∈ A p loc (? n ) on a d-dimensional plane for 1 ≤ d < n. It turns out that for a function φ to be the trace of a function f ∈ W p l (? n , γ), it is necessary and sufficient that φ belongs to a new Besov space of variable smoothness, $\overline B _p^l \left( {\mathbb{R}^d ,\left\{ {\gamma _{k,m} } \right\}} \right)$ , constructed in this paper. The space $\overline B _p^l \left( {\mathbb{R}^d ,\left\{ {\gamma _{k,m} } \right\}} \right)$ is compared with some earlier known Besov spaces of variable smoothness. 相似文献
9.
Let \(\chi _0^n = \left\{ {X_t } \right\}_0^n \) be a martingale such that 0≦Xi≦1;i=0, …,n. For 0≦p≦1 denote by ? p n the set of all such martingales satisfying alsoE(X0)=p. Thevariation of a martingale χ 0 n is denoted byV 0 n and defined by \(V(\chi _0^n ) = E\left( {\sum {_{l = 0}^{n - 1} } \left| {X_{l + 1} - X_l } \right|} \right)\) . It is proved that $$\mathop {\lim }\limits_{n \to \infty } \left\{ {\mathop {Sup}\limits_{x_0^n \in \mathcal{M}_p^n } \left[ {\frac{1}{{\sqrt n }}V(\chi _0^n )} \right]} \right\} = \phi (p)$$ , where ?(p) is the well known normal density evaluated at itsp-quantile, i.e. $$\phi (p) = \frac{1}{{\sqrt {2\pi } }}\exp ( - \frac{1}{2}\chi _p^2 ) where \int_{ - \alpha }^{x_p } {\frac{1}{{\sqrt {2\pi } }}\exp ( - \frac{1}{2}\chi ^2 )} dx = p$$ . A sequence of martingales χ 0 n ,n=1,2, … is constructed so as to satisfy \(\lim _{n \to \infty } (1/\sqrt n )V(\chi _0^n ) = \phi (p)\) . 相似文献
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A. M. Raigorodskii 《Combinatorica》2012,32(1):111-123
Let χ(S r n?1 )) be the minimum number of colours needed to colour the points of a sphere S r n?1 of radius $r \geqslant \tfrac{1} {2}$ in ? n so that any two points at the distance 1 apart receive different colours. In 1981 P. Erd?s conjectured that χ(S r n?1 )→∞ for all $r \geqslant \tfrac{1} {2}$ . This conjecture was proved in 1983 by L. Lovász who showed in [11] that χ(S r n?1 ) ≥ n. In the same paper, Lovász claimed that if $r < \sqrt {\frac{n} {{2n + 2}}}$ , then χ(S r n?1 ) ≤ n+1, and he conjectured that χ(S r n?1 ) grows exponentially, provided $r \geqslant \sqrt {\frac{n} {{2n + 2}}}$ . In this paper, we show that Lovász’ claim is wrong and his conjecture is true: actually we prove that the quantity χ(S r n?1 ) grows exponentially for any $r > \tfrac{1} {2}$ . 相似文献
12.
E. Semyonov 《Integral Equations and Operator Theory》1983,6(1):385-404
Operators of the form Tπχ n k =χ n πn(k) where {χ n k (t)} is the Haar system and πn is a rearrangement of the numbers 1,2, ?.2n (n=1,2,?) are studied. Criterion for the boundedness of such operators from the spaceL p intoL p is obtained. 相似文献
13.
I. I. Sharapudinov 《Mathematical Notes》2013,94(1-2):281-293
We study new series of the form $\sum\nolimits_{k = 0}^\infty {f_k^{ - 1} \hat P_k^{ - 1} (x)} $ in which the general term $f_k^{ - 1} \hat P_k^{ - 1} (x)$ , k = 0, 1, …, is obtained by passing to the limit as α→?1 from the general term $\hat f_k^\alpha \hat P_k^{\alpha ,\alpha } (x)$ of the Fourier series $\sum\nolimits_{k = 0}^\infty {f_k^\alpha \hat P_k^{\alpha ,\alpha } (x)} $ in Jacobi ultraspherical polynomials $\hat P_k^{\alpha ,\alpha } (x)$ generating, for α> ?1, an orthonormal system with weight (1 ? x 2)α on [?1, 1]. We study the properties of the partial sums $S_n^{ - 1} (f,x) = \sum\nolimits_{k = 0}^n {f_k^{ - 1} \hat P_k^{ - 1} (x)} $ of the limit ultraspherical series $\sum\nolimits_{k = 0}^\infty {f_k^{ - 1} \hat P_k^{ - 1} (x)} $ . In particular, it is shown that the operator S n ?1 (f) = S n ?1 (f, x) is the projection onto the subspace of algebraic polynomials p n = p n (x) of degree at most n, i.e., S n (p n ) = p n ; in addition, S n ?1 (f, x) coincides with f(x) at the endpoints ±1, i.e., S n ?1 (f,±1) = f(±1). It is proved that the Lebesgue function Λ n (x) of the partial sums S n ?1 (f, x) is of the order of growth equal to O(ln n), and, more precisely, it is proved that $\Lambda _n (x) \leqslant c(1 + \ln (1 + n\sqrt {1 - x^2 } )), - 1 \leqslant x \leqslant 1$ . 相似文献
14.
Abdellah Youssfi 《manuscripta mathematica》1989,65(3):289-310
Our purpose is to give necessary and sufficient conditions for continuity, on Besov spaces \(\dot B_p^{s,q} \) , of singular integral operators whose kernels satisfy: $$|\partial _x^\alpha K(x, y)| \leqslant C_\alpha |x - y|^{ - n - |\alpha |} for|\alpha | \leqslant m,$$ where m ∈ ? and 0 < s < m. The criterion is compared to the M.Meyer theorem [11] where 0 p s,q spaces for s?1. For 0 p s,p space is characterized by the localization and by Besov-capacity. In particular we show that the BMO 1 s,1 space is characterized by generalized Carleson conditions. 相似文献
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S. G. Pribegin 《Mathematical Notes》2007,82(5-6):643-652
Suppose that H p (E 2n + ) is the Hardy space for the first octant $$E_{2n}^ + = \{ z \in \mathbb{C}^n :\operatorname{Im} z_j > 0, j = 1, \ldots ,n\} $$ and P ? l (f, x), l > 0, is the generalized Abel-Poisson means of a function f ? H p (E 2n + ). In this paper, we prove the inequalities $$C_1 (l,p)\widetilde\omega _l (\varepsilon ,f)_p \leqslant \left\| {f(x) - P_\varepsilon ^l (f,x)} \right\|_p \leqslant C_2 (l,p)\omega _l (\varepsilon ,f)_p ,$$ where $\widetilde\omega _l (\varepsilon ,f)_p $ and ω l (?, f) p are the integral moduli of continuity of lth order. For n = 1 and an integer l, this result was obtained by Soljanik. 相似文献
16.
We prove that the fundamental semi-group eit(m 2I+|Δ|)1/2(m = 0) of the Klein-Gordon equation is bounded on the modulation space M ps,q(Rn) for all 0 < p,q ∞ and s ∈ R.Similarly,we prove that the wave semi-group eit|Δ|1/2 is bounded on the Hardy type modulation spaces μsp,q(Rn) for all 0 < p,q ∞,and s ∈ R.All the bounds have an asymptotic factor tn|1/p 1/2| as t goes to the infinity.These results extend some known results for the case of p 1.Also,some applications for the Cauchy problems related to the semi-group eit(m2I+|Δ|)1/2 are obtained.Finally we discuss the optimum of the factor tn|1/p 1/2| and raise some unsolved problems. 相似文献
17.
Z. J. Jabłoński 《Acta Mathematica Hungarica》2008,120(1-2):21-28
Given a family $ \{ A_m^x \} _{\mathop {m \in \mathbb{Z}_ + ^d }\limits_{x \in X} } $ (X is a non-empty set) of bounded linear operators between the complex inner product space $ \mathcal{D} $ and the complex Hilbert space ? we characterize the existence of completely hyperexpansive d-tuples T = (T 1, … , T d ) on ? such that A m x = T m A 0 x for all m ? ? + d and x ? X. 相似文献
18.
In the space L 2[0, π], we consider the operators $$ L = L_0 + V, L_0 = - y'' + (\nu ^2 - 1/4)r^{ - 2} y (\nu \geqslant 1/2) $$ with the Dirichlet boundary conditions. The potential V is the operator of multiplication by a function (in general, complex-valued) in L 2[0, π] satisfying the condition $$ \int\limits_0^\pi {r^\varepsilon } (\pi - r)^\varepsilon |V(r)|dr < \infty , \varepsilon \in [0,1] $$ . We prove the trace formula Σ n=1 ∞ [µ n ? λ n ? Σ k=1 m α k (n) ] = 0. 相似文献
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Yu. N. Kuznetsova 《Mathematical Notes》2008,84(3-4):529-537
The paper is devoted to weighted spaces ? p w (G) on a locally compact group G. If w is a positive measurable function on G, then the space ? p w (G), p ≥ 1, is defined by the relation ? p w (G) = {f: fw ∈ ? p (G)}. The weights w for which these spaces are algebras with respect to the ordinary convolution are treated. It is shown that, for p > 1, every sigma-compact group admits a weight defining such an algebra. The following criterion is proved (which was known earlier for special cases only): a space ? p w (G) is an algebra if and only if the function w is semimultiplicative. It is proved that the invariance of the space ? p w (G) with respect to translations is a sufficient condition for the existence of an approximate identity in the algebra ? p w (G). It is also shown that, for a nondiscrete group G and for p > 1, no approximate identity of an invariant weighted algebra can be bounded. 相似文献
20.
I. Joó 《Analysis Mathematica》1975,1(4):273-281
В этой работе мы даем о бобщение понятия нор мальной системы точек, введен ного Фейером [3]. Наше определ ение включает и случа й бесконечного интерв ала (0, ∞). Доказано, в частности, что систе ма точек 0<x 1 (n) /(n)<... n (n) <∞ является нормальной в смысле нашего определения тогда и т олько тогда, когда вып олняются оценки — фиксированное чис ло, 0≦?<1. Мы доказываем, что есл и точкиx k (n) /(n) являются ну лями многочлена ЛагерраL n (α) (x), то они образуют норма льную систему в том и т олько том случае, когда ?1<α≦0. Мы получаем, таким обр азом, положительный интерполяционный пр оцесс для каждой нормальной системы т очек и устанавливаем теорему сходимости для того с лучая, когда эти точки являются ну лямиL n (α) (x) при — 1相似文献