共查询到20条相似文献,搜索用时 46 毫秒
1.
We show that certain functional inequalities, e.g. Nash-type and Poincaré-type inequalities, for infinitesimal generators of C 0 semigroups are preserved under subordination in the sense of Bochner. Our result improves earlier results by Bendikov and Maheux (Trans Am Math Soc 359:3085–3097, 2007, Theorem 1.3) for fractional powers, and it also holds for non-symmetric settings. As an application, we will derive hypercontractivity, supercontractivity and ultracontractivity of subordinate semigroups. 相似文献
2.
Let Ω be a smooth bounded domain in , . We show that Hardy's inequality involving the distance to the boundary, with best constant (), may still be improved by adding a multiple of the critical Sobolev norm. To cite this article: S. Filippas et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
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We show that fractional (p, p)-Poincaré inequalities and even fractional Sobolev-Poincaré inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. We also prove sharp fractional (1,p)-Poincaré inequalities for s-John domains. 相似文献
5.
Dalia Bolotnikov 《Linear and Multilinear Algebra》2013,61(2):249-254
C. Cowen and C. Pommerenke established inequalities for the derivatives of analytic self-mappings of the open unit disk at their fixed points. In this article, we show that these inequalities can be derived from Schwarz–Pick inequalities 相似文献
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LIU Zhenhai & ZOU Jiezhong Department of Mathematics Changsha University of Science Technology Changsha China School of Mathematical Science Computing Technology Central South University Changsha China 《中国科学A辑(英文版)》2006,49(7):893-901
The purpose of this paper is to study a regularization method of solutions of ill-posed problems involving hemivariational inequalities in Banach spaces. Under the assumption that the hemivariational inequality is solvable, a strongly convergent approximation procedure is designed by means of the so-called Browder-Tikhonov regularization method. Our results generalize and extend the previously known theorems. 相似文献
8.
Ta Lê Loi 《manuscripta mathematica》2016,150(1-2):59-72
This note is devoted to the generalization of ?ojasiewicz inequalities for functions definable in o-minimal structures, which is, roughly speaking, a generalization for semialgebraic or global subanalytic functions. We present some o-minimal versions of the inequalities to compare two definable functions globally or in some neighborhoods of the zero-sets of the functions, and the gradient inequalities (Kurdyka–?ojasiewicz inequality and Bochnak–?ojasiewicz inequality). Some applications of the inequalities are given. 相似文献
9.
G. Kós 《Acta Mathematica Hungarica》2008,119(3):219-226
Turán’s book [2], in Section 19.4, refers to the following result of Gábor Halász. Let a
0, a
1, ..., a
n−1 be complex numbers such that the roots α
1, ⋯, α
n
of the polynomial x
n
+ a
n−1
x
n−1 + ⋯ + a
1
x + a
0 satisfy min
j
Re α
j
≧ 0 and let function Y(t) be a solution of the linear differential equation Y
(n) + a
n−1
Y
(n−1) + ⋯ + a
1
Y′ + a
0
Y = 0. Then
In particular, (1) holds for polynomials of degree at most n − 1 and functions of the form where b
1,..., b
n
are arbitrary complex numbers and Re α
j
≧ 0.
In this paper we improve the exponent 5 on the right-hand side to the best possible value (which is 2) and prove an analogous
inequality where the integration domain is symmetric to the origin.
This research has been supported by the János Bolyai Grant of the Hungarian Academy of Sciences. 相似文献
((1)) |
10.
A criterion for algebraic convergence of the entropy is presented and an algebraic convergence result for the entropy of an exclusion process is improved. A weak entropy inequality is considered and its relationship to entropic convergence is discussed. 相似文献
11.
Joseph Lehec 《Archiv der Mathematik》2009,92(1):89-94
We give a direct proof of a functional Santaló inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santaló
inequality. The argument combines a logarithmic form of the Prékopa-Leindler inequality and a partition theorem of Yao and
Yao.
Received: 21 August 2008 相似文献
12.
New sharp Lorentz–Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the L
p
Minkowski problem. New L
p
isocapacitary and isoperimetric inequalities are proved for Lipschitz star bodies. It is shown that the sharp convex Lorentz–Sobolev
inequalities are analytic analogues of isocapacitary and isoperimetric inequalities. 相似文献
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George A. Anastassiou 《Applicable analysis》2013,92(8):945-961
In this article we present very general weighted Hilbert–Pachpatte type integral inequalities. These are regarding ordinary derivatives and fractional derivatives of Riemann–Liouiville and Canavati types. Also regarding general derivatives of Widder type and linear differential operators. Our results apply to continuous functions and some to integrable functions. 相似文献
17.
Clément Mouhot Emmanuel Russ Yannick Sire 《Journal de Mathématiques Pures et Appliquées》2011,95(1):72-84
We prove a fractional version of Poincaré inequalities in the context of endowed with a fairly general measure. Namely we prove a control of an norm by a non-local quantity, which plays the role of the gradient in the standard Poincaré inequality. The assumption on the measure is the fact that it satisfies the classical Poincaré inequality, so that our result is an improvement of the latter inequality. Moreover we also quantify the tightness at infinity provided by the control on the fractional derivative in terms of a weight growing at infinity. The proof goes through the introduction of the generator of the Ornstein–Uhlenbeck semigroup and some careful estimates of its powers. To our knowledge this is the first proof of fractional Poincaré inequality for measures more general than Lévy measures. 相似文献
18.
George A. Anastassiou 《Mathematical and Computer Modelling》2009,49(7-8):1539-1550
We present here very general weighted univariate and multivariate Hilbert–Pachpatte type integral inequalities. These involve Caputo and Riemann–Liouville fractional derivatives and fractional partial derivatives of the mentioned types. 相似文献
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20.
For the potential type operator
TФf(x)=∫RnФ(x-y)f(y)dy,
where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type (p,q) inequality for TФ is obtained. 相似文献
TФf(x)=∫RnФ(x-y)f(y)dy,
where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type (p,q) inequality for TФ is obtained. 相似文献