共查询到17条相似文献,搜索用时 87 毫秒
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研究非凸区域上的Hardy型不等式.通过选取特殊的向量值函数以及仔细的分析与计算,得到了各向异性Heisenberg群上一类非凸区域上的Hardy不等式,更进一步得到了非凸区域上与Greiner型向量场相关的几类Hardy型不等式. 相似文献
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利用一些非常精细的估计技巧,证明了各向异性Heisenberg群上的一类带余项的Hardy型不等式,推广了最近文献中关于Heisenberg群上的带余项的Hardy型不等式的结果. 相似文献
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采用Badiale和Tarantello在R~n上建立Hardy-Sobolev不等式的思想,首先建立各向异性Heisenberg群上的函数表示公式,给出一类Hardy型不等式;然后利用Hlder不等式和Sobolev不等式,通过插值给出各向异性Heisenberg群上的Hardy-Sobolev型不等式.结合Lions的集中列紧原理的思想,得到Hardy-Sobolev型不等式极值函数的存在性. 相似文献
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证明了一类海森堡群上半空间内与次拉普拉斯算子相关的最佳Hardy不等式.作为应用,我们得到了相应的最佳Rellich型不等式. 相似文献
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本文研究Hardy型不等式及它的应用.首先从Heisenberg群上加权次椭圆p-Laplace不等方程出发,得到非负Lipschitz函数的Caccioppoli不等式,然后利用该不等式导出了关于另一Lipschitz函数的Hardy型不等式,进而推出一个精确Hardy-Poincare不等式.需要强调的是,我们这里的Hardy型不等式是对于1
相似文献
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本文在Heisenberg型群上建立了一类精确的Hardy型不等式。采用的技巧是逼近及正则化的方法。进一步利用这个结果,本文建立了一类精确的Hardy-Sobolev型不等式。这两个结果包括了已有的相关结果。作为应用,讨论了一类具有Hardy位势的非线性算子的正定性与下无界性。 相似文献
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给出四元素Heisenberg群上次Laplace算子的平均值定理,并用其导出Hardy不等式和不确定原理. 相似文献
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We prove a Hardy type inequality in the half-space on the Heisenberg group and show that a Hardy inequality given by J. Tidblm in [J. Tidblm, A Hardy inequality in the half-space, J. Funct. Anal. 221 (2005) 482–492] is sharp. 相似文献
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In the setting of the Heisenberg group, based on the rotation method, we obtain the sharp (p, p) estimate for the Hardy operator. It will be shown that the norm of the Hardy operator on Lp(H n) is still p/(p−1). This goes some way to imply that the Lp norms of the Hardy operator are the same despite the domains are intervals on ℝ, balls in ℝn, or ‘ellipsoids’ on the Heisenberg group H n. By constructing a special function, we find the best constant in the weak type (1,1) inequality for the Hardy operator. Using the translation approach, we establish the boundedness for the Hardy operator from H1 to L1. Moreover, we describe the difference between Mp weights and Ap weights and obtain the characterizations of such weights using the weighted Hardy inequalities. 相似文献
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In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg
group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of
Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,
we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined. 相似文献
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Jingxuan Fang & Jiman Zhao 《分析论及其应用》2016,32(3):242-271
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators. 相似文献
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Hardy type and Rellich type inequalities on the Heisenberg group 总被引:13,自引:0,他引:13
Pengcheng Niu Huiqing Zhang Yong Wang 《Proceedings of the American Mathematical Society》2001,129(12):3623-3630
This paper contains some interesting Hardy type inequalities and Rellich type inequalities for the left invariant vector fields on the Heisenberg group.
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The heat kernel transform Ht is studied for the Heisenberg group in detail. The main result shows that the image of Ht is a direct sum of two weighted Bergman spaces, in contrast to the classical case of Rn and compact symmetric spaces, and the weight functions are found to be (surprisingly) not non-negative. 相似文献