俄罗斯数学家最近证明了一个重要的数学不等式。这个成果具有重要的数学和物理学意义。所提供的新的数学工具可以大大简化量子力学和其他物理领域的计算。该研究成果发表在最近的《 数学札记》杂志上。 这个数学不等式的名字叫哈代–利特伍德–索博列夫不等式(Hardy-Littlewood-Sobolev inequality,简称HLS不等式)。下面我们尽...
Hardy-Littlewood-Sobolev inequalityRestrictive Sobolev inequalityStability of Sobolev trace inequalityIn this paper, we establish the stability for the Hardy-Littlewood-Sobolev (HLS) inequalities with explicit lower bounds. By establishing the relation between the stability of HLS inequalities and the ...
一类带有Hardy-Littlewood-Sobolev下临界指数的非线性Choquard方程多解的 Affine structure on the Teichmuller spaces and period maps for Calabi-Yau manifolds Differential and Integral Inequalities Theory and Applications, Vol. 2 Functional Partial, Abstract and Complex Differential Equations 2004-Peter LI__Harmo...
Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy-Littlewood-Sobolev inequality on general homogeneous Lie groups.doi:10.48550/arXiv.1810.11439Aidyn KassymovMichael RuzhanskyDurvudkhan Suragan...
Hardy–Littlewood–Sobolev inequality42B3542B2542B10We introduce the Riesz potential associated with the Weinstein operator of order s , as where is its heat semigroup. Next, we define the fractional Littlewood–Paley g -function denoted of order s , as where is the Poisson integral of f . ...
Olsen inequalityWe establish in this paper the Hardy-Littlewood-Sobolev inequalities for the Riesz potentials on Morrey spaces over commutative hypergroups. As a consequence, we are also able to get Olsen-type inequality on the same spaces. Here, the condition of upper Ahlfors n-regular by ...
In this note we combine semigroup theory with a nonlocal calculus for these hypoelliptic operators to establish new inequalities of Hardy–Littlewood–Sobolev type in the situation when the drift matrix has nonnegative trace. Our work has been influenced by ideas of E. Stein and Varopoulos in ...
有界和弱(1,1)有界的,即证明K上的Hardy-Littlewood— Sobolev不 等式.它为进一步分析K上的偏微分方程问题提供了一个有利的工具. 关键词Laguerre超群;Hardy-Iittlewood—Sobolev不等式;热核 分类号01741 经典的Riesz位势在调和分析和偏微分 方程中具有重要的作用.经典的Riesz位 势由拉普拉斯算子来定义,K.Stempak[...
(1|x|μ∗u2μ∗)v2μ∗−1,x∈Ω,u,v≥0inΩ,u=v=0on∂Ω,where Ω⊂RN is a smooth bounded domain, ≔2μ∗≔2N−μN−2 is the critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality, −λ1(Ω)<λ1,λ2<0,λ1(Ω) is the first eigen...
In this paper, we study the best constant of the following discrete Hardy-Littlewood-Sobolev inequality, \\\begin{equation} \\\sum_{i,j,ieq j}\\\frac{f_{i}g_{j}}{\\\mid i-j\\\mid^{n-\\\alpha}}\\\leq C_{r,s,\\\alpha} |f|_{l^r} |g|_{l^s}, \\\end{equation}w...