共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article we obtain a duality result for an n-manifold N with boundary ∂N = N + ⊔N
−
a disjoint union, where N
+ and N
−
are arbitrarily chosen parts in ∂N and need not be compact. This duality result is used to generalize the Poincaré–Hopf inequalities in a non-compact setting. 相似文献
2.
S. V. Nagaev 《Acta Appl Math》2007,97(1-3):151-162
Burkholder’s type inequality is stated for the special class of martingales, namely the product of independent random variables. The constants in the latter are much less than in the general case which is considered in Nagaev (Acta Appl. Math. 79, 35–46, 2003; Teor. Veroyatn. i Primenen. 51(2), 391–400, 2006). On the other hand, the moment inequality is proved, which extends these by Wittle (Teor. Veroyatn. i Primenen. 5(3), 331–334, 1960) and Dharmadhikari and Jogdeo (Ann. Math. Stat. 40(4), 1506–1508, 1969) to martingales. 相似文献
3.
Feng-Yu Wang 《Potential Analysis》2005,22(1):1-15
A generalized Beckner-type inequality interpolating the Poincaré and the log-Sobolev inequalities is studied. This inequality possesses the additivity property and characterizes certain exponential convergence of the corresponding Markov semi-group. A correspondence between this inequality and the so-called F-Sobolev inequality is presented, with the known criteria of the latter applying also to the former. In particular, an important result of Lataa and Oleszkiewicz is generalized. 相似文献
4.
V. I. Ivanov 《Journal of Optimization Theory and Applications》2010,146(3):602-616
In the present paper we consider a pseudoconvex (in an extended sense) function f using higher order Dini directional derivatives. A Variational Inequality, which is a refinement of the Stampacchia Variational
Inequality, is defined. We prove that the solution set of this problem coincides with the set of global minimizers of f if and only if f is pseudoconvex. We introduce a notion of pseudomonotone Dini directional derivatives (in an extended sense). It is applied
to prove that the solution sets of the Stampacchia Variational Inequality and Minty Variational Inequality coincide if and
only if the function is pseudoconvex. At last, we obtain several characterizations of the solution set of a program with a
pseudoconvex objective function. 相似文献
5.
InequalitiesInvolvingHadamardProductsandUnitarilyInvariantNormsZhanXingzhi(詹兴致)(InstituteofMathematics,PekingUniversity,Beiji... 相似文献
6.
Ⅰ. Introduction Let (a_(1j), a_(2j),…, a_(t_jj_)(1≤j≤k) be sequences of length, where a_(ij)≥0 and n= be the arranged in non-dec reasingorde:and; and be the a_(ij)(1≤i≤t_j; 1≤j≤k) arranged in non-increasing order: We also write 相似文献
7.
In Martín et al. (J Funct Anal 252:677–695, 2007) we developed a new method to obtain symmetrization inequalities of Sobolev type for functions in . In this paper we extend our method to Sobolev functions that do not vanish at the boundary.
This paper is in final form and no version of it will be submitted for publication elsewhere. 相似文献
8.
Denis SERRE 《数学年刊B辑(英文版)》2009,30(6):785-802
The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices, after a conjecture by A. Horn. Among them are the so-called Weyl and Lidskiǐ inequalities. An elementary proof of the latter for hyperbolic polynomials is given. This proof follows an idea from H. Weinberger and is free from representation theory and Schubert calculus arguments, as well as from hyperbolic partial differential equations theory. 相似文献
9.
ANoteon"RearrangementandMatrixProductInequalities"YangZhongpeng(杨忠鹏)(DepartmentMathematics,JilinTeacher'sCollege,Jilin,132011... 相似文献
10.
11.
We consider weighted inequalities such as Bernstein, Nikolskii, Remez, etc., inequalities under minimal assumptions on the
weights. It turns out that in most cases this mimimal assumption is the doubling condition. Sometimes, however, as for the
Remez and Nikolskii inequalities, one needs the slightly stronger A
∈
fty condition. We shall consider both the trigonometric and the algebraic cases.
August 20, 1997. Date revised: April 19, 1998. Date accepted: May 26, 1998. 相似文献
12.
In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb–Thirring inequality for anyons in two dimensions, and derive new Lieb–Thirring inequalities for intermediate statistics in one dimension with implications for models of Lieb–Liniger and Calogero–Sutherland type. These inequalities follow from a local form of the exclusion principle valid for such generalized exchange statistics. 相似文献
13.
Frédéric Bernicot Diego Maldonado Kabe Moen Virginia Naibo 《Journal of Geometric Analysis》2014,24(2):1144-1180
The dual purpose of this article is to establish bilinear Poincaré-type estimates associated with an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato–Morrey spaces under Sobolev scaling. 相似文献
14.
Fernando GIMENEZ Javier Orengo VALVERDE 《数学学报(英文版)》2007,23(7):1317-1326
On surfaces we give conditions under which the solution of a restricted local isoperimetric problem for sectors with small solid angle is the circular sector and we characterize these surfaces. Also we study this problem for general spherical cones on hypersurfaces in higher dimensional Riemannian manifolds. 相似文献
15.
Oliver Kley 《Journal of Theoretical Probability》2013,26(3):649-665
Let T be a precompact subset of a Hilbert space. We make use of a precise link between the absolutely convex hull $\operatorname{aco}(T)$ and the reproducing kernel Hilbert space of a Gaussian random variable constructed from T. Firstly, we avail ourselves of it for optimality considerations concerning the well-known Kuelbs–Li inequalities. Secondly, this enables us to apply small deviation results to the problem of estimating the metric entropy of $\operatorname{aco}(T)$ in dependence of the metric entropy of T. 相似文献
16.
Jae Hyoung Lee Gue Myung Lee Tiến-Sơn Phạm 《Journal of Optimization Theory and Applications》2018,178(1):56-77
The aim of this paper is twofold. We first present generic properties of semi-algebraic variational inequalities: “typical” semi-algebraic variational inequalities have finitely many solutions, around each of which they admit a unique “active manifold” and such solutions are nondegenerate. Second, based on these results, we offer Hölder stability, upper semi-continuity, and lower semi-continuity properties of the solution map of parameterized variational inequalities. 相似文献
17.
5l.TheMedianFormulaAseveryoneknows:in6ABC,letal=BC,a2=CA,a3=AB,;)11,)n2,n13aremedian1inesseparatelyonthethreeedgesBC,CA,AB,tI1entheequalityistrueasfollowsTheequality(l)iscalledmedianformulaofQABC,andwecanobtainfrom(l)Inthispaper,wesha1lextendtheequality(l)and(2)to,l-simplexin)l-EuclideanspaceH.Itisobtainedthemedianformulaof)I-simplex,andusingthisformula.wegetsomein-equalities.Themedianformulaofn-simp1exisobtainedasfollows:TheoremlFork=1,2,--',It 1andl相似文献
18.
Let f be in the localized nonisotropic Sobolev space
on the n-dimensional
Heisenberg group ℍ
n
= ℂ
n
× ℝ, where 1 = p < Q and Q = 2n + 2 is the homogeneous dimension
of ℍn. Suppose that the subelliptic gradient is gloablly L
p
integrable, i.e.,
is finite.
We prove a Poincaré inequality for f on the entire space ℍ
n
. Using this inequality we prove that the
function f subtracting a certain constant is in the nonisotropic Sobolev space formed by the completion
of
under the norm of
We will also prove that the best constants and extremals for such Poincaré inequalities on ℍ
n
are
the same as those for Sobolev inequalities on ℍ
n
. Using the results of Jerison and Lee on the sharp
constant and extremals for L
2 to
Sobolev inequality on the Heisenberg group, we thus arrive
at the explicit best constant for the aforementioned Poincaré inequality on ℍ
n
when p = 2. We also
derive the lower bound of the best constants for local Poincaré inequalities over metric balls on the
Heisenberg group ℍ
n
.
The first author is supported by Zhongdian grant of NSFC; The second author is supported by a global grant at Wayne State
University and by NSF of USA 相似文献
19.
Zoltán M. Balogh Alexandre Engulatov Lars Hunziker Outi Elina Maasalo 《Potential Analysis》2012,36(2):317-337
We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p ≥ 2, q ≤ 2 in proper geodesic metric spaces. By means of a general Hamilton–Jacobi semigroup we prove that these are equivalent,
and moreover equivalent to the hypercontractivity of the Hamilton–Jacobi semigroup. Our results generalize those of Lott and
Villani. They can be applied to deduce the p-Talagrand inequality in the sub-Riemannian setting of the Heisenberg group. 相似文献
20.
Pierre-André Zitt 《Potential Analysis》2011,35(1):51-66
We prove some results about the super Poincaré inequality (SPI) and its relation to the spectrum of an operator: we show that
it can be alternatively written with Orlicz norms instead of L
1 norms, and we use this to give an alternative proof that a bound on the bottom of the essential spectrum implies a SPI. Finally,
we apply these ideas to give a spectral proof of the log Sobolev inequality for the Gaussian measure. 相似文献