Pablo L. De Nápoli, Irene Drelichman, Ricardo G. Durán
We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in $\mathbb{R}^n \times \mathbb{R}_+$ admit a better range of power weights if we restrict ourselves to the space of radially symmetric functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We set up a one-parameter family of inequalities that contains both the Hardy inequalities (when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the parameter is optimal). Moreover, we study these results with the exact remainders to provide direct understandings to the sharp constants, as well as the existence and non-existence of the optimizers of the Hardy inequalities and Caffarelli-Kohn-Nirenberg inequalities. As an application of our identities, we establish some sharp versions with optimal constants and theirs attainability of the stability of the Heisenberg Unc…
We prove an extension of the Stein-Weiss weighted estimates for fractional integrals, in the context of $L^{p}$ spaces with different integrability properties in the radial and the angular direction. In this way, the classical estimates can be unified with their improved radial versions. A number of consequences are obtained: in particular we deduce precised versions of weighted Sobolev embeddings, Caffarelli-Kohn-Nirenberg estimates, and Strichartz estimates for the wave equation, which extend the radial improvements to the case of arbitrary functions.
We prove that for the Navier Stokes equation with dissipation $(-Δ)^α$, where $1<α<{5/4}$, and smooth initial data, the Hausdorff dimension of the singular set at time of first blow up is at most $5-4α$. This unifies two directions from which one might approach the Clay prize problem.
Caffarelli-Kohn-Nirenberg Inequalities in Weak Lebesgue Spaces
本文通过调和分析技术推导出在临界参数条件下仍有效的弱型Caffarelli-Kohn-Nirenberg不等式，并获得了在临界维度下成立的弱型Hardy不等式。
In this paper, we will use a suitable tranform to investigate the sharp constants and optimizers for the following Caffarelli-Kohn-Nirenberg inequalities for a wide range of parameters $(r,p,q,s,μ,σ)$ and $0\leq a\leq1$: \begin{equation} \left({\displaystyle\int} \left\vert u\right\vert ^{r}\frac{dx}{\left\vert x\right\vert ^{s}}\right)^{1/r}\leq C\left( {\displaystyle\int} \left\vert \nabla u\right\vert ^{p}\frac{dx}{\left\vert x\right\vert ^μ% }\right) ^{a/p}\left({\displaystyle\int} \left\vert u\right\vert ^{q}\frac{dx}{\left\vert x\right\vert ^σ% }\right) ^{\left( 1-a\right) /q}. \end{equa…
In the setting of a Lie group of polynomial volume growth, we derive inequalities of Caffarelli-Kohn-Nirenberg type, where the weights involved are powers of the Carnot-Caratheodory distance associated with a fixed system of vector fields which satisfy the Hörmander condition. The use of weak $L^p$ spaces is crucial in our proofs and we formulate these inequalities within the framework of $L^{p,q}$ Lorentz spaces (a scale of (quasi)-Banach spaces which extend the more classical $L^p$ Lebesgue spaces) thereby obtaining a refinement of, for instance, Sobolev and Hardy-Sobolev inequalities.
Anisotropic Caffarelli-Kohn-Nirenberg inequalities with higher-order fractional derivatives
证明了一族涉及高阶分数阶导数和形如$|x'|^{\theta_1}|x|^{\theta_2}|x_n|^{\theta_3}$权重的各向异性Caffarelli-Kohn-Nirenberg插值不等式。
We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps from a sphere into itself and characterizations of Sobolev spaces.
Optimal stability hierarchies of the Heisenberg Uncertainty Principle for solenoidal fields and of the second order Caffarelli--Kohn--Nirenberg inequalities
本文针对螺线管场的海森堡不确定性原理和二阶CKN不等式，建立了最优稳定性层级，给出显式稳定性常数，并通过Fourier--Hankel变换新方法简化证明。
Recent sampling theorems allow for the recovery of operators with bandlimited Kohn-Nirenberg symbols from their response to a single discretely supported identifier signal. The available results are inherently non-local. For example, we show that in order to recover a bandlimited operator precisely, the identifier cannot decay in time nor in frequency. Moreover, a concept of local and discrete representation is missing from the theory. In this paper, we develop tools that address these shortcomings. We show that to obtain a local approximation of an operator, it is sufficient to test the opera…
Weighted Gagliardo-Nirenberg Interpolation Inequalities
本文通过调和分析中的稀疏算子控制等方法，证明了带Riesz和Bessel型分数阶导数的加权Gagliardo-Nirenberg插值不等式，推广了Stein-Weiss和Caffarelli-Kohn-Nirenberg不等式，并适用于幂律及Japanese括号等权重。
We study the geometry of $m$-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every $m$-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly $m$-subharmonic, and has bounded $m$-Hessian measure.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。