论文标题
涉及单数电位的紧凑型歧管上的均匀索波列夫估计值
Uniform Sobolev Estimates on compact manifolds involving singular potentials
论文作者
论文摘要
We obtain generalizations of the uniform Sobolev inequalities of Kenig, Ruiz and the fourth author \cite{KRS} for Euclidean spaces and Dos Santos Ferreira, Kenig and Salo \cite{DKS} for compact Riemannian manifolds involving critically singular potentials $V\in L^{n/2}$.我们还获得了第一个，第三和第四作者的类似改进的准杂志估计值\ cite {bss}，hassell and tacy \ cite \ cite {hasselltacy}，第一和第四作者\ cite \ cite {sblog}，以及希克曼\ cite \ cite {hickman}以及估计{hickman}的估计，以及相对的unibore nud。 \ cite {bssy}和\ cite {hickman}涉及此类潜力。此外，在$ s^n $上，我们获得了涉及最佳指数范围的此类潜力的尖锐统一的sobolev不等式，这些范围扩展了黄链链菌的结果和第四作者\ cite \ cite {shso}。对于一般的riemannian歧管，我们通过在较大（且最佳）范围的指数范围中获得较大（和最佳的）指数范围的Quasimode估计值在较弱的假设中，即$ v \ in l^{n/2} $中的较弱的假设。
We obtain generalizations of the uniform Sobolev inequalities of Kenig, Ruiz and the fourth author \cite{KRS} for Euclidean spaces and Dos Santos Ferreira, Kenig and Salo \cite{DKS} for compact Riemannian manifolds involving critically singular potentials $V\in L^{n/2}$. We also obtain the analogous improved quasimode estimates of the the first, third and fourth authors \cite{BSS} , Hassell and Tacy \cite{HassellTacy}, the first and fourth author \cite{SBLog}, and Hickman \cite{Hickman} as well as analogues of the improved uniform Sobolev estimates of \cite{BSSY} and \cite{Hickman} involving such potentials. Additionally, on $S^n$, we obtain sharp uniform Sobolev inequalities involving such potentials for the optimal range of exponents, which extend the results of S. Huang and the fourth author \cite{SHSo}. For general Riemannian manifolds we improve the earlier results in \cite{BSS} by obtaining quasimode estimates for a larger (and optimal) range of exponents under the weaker assumption that $V\in L^{n/2}$.
