Related papers: Compactness methods in Lieb's work
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…
We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…
We present unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Poly\'a and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp…
The given study uses the methods to identify compactifications of semigroups $S\subset L(X),$ which reside in the space $L(X).$ This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The…
In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of…
In this paper we are focusing on functional inequalities on compact simple edge spaces. More precisely we address the question whether the classical functional inequalities (Sobolev, Poincar\'e) hold in this setting, and as a by-product of…
A fundamental tool in the analysis of Ricci flow is a compactness result of Hamilton in the spirit of the work of Cheeger, Gromov and others. Roughly speaking it allows one to take a sequence of Ricci flows with uniformly bounded curvature…
We prove sharp inequalities of Hardy type for functions in the Sobolev space $W^{1,p}$ on the unit sphere $\mathbb{S}^{n-1}$ in $\mathbb{R}^{n}$. We achieve this in both the subcritical and critical cases. The method we use to show…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this paper, we study the properties of closure operators obtained as initial lifts along a reflector, and compactness with respect to them in particular. Applications in the areas of topology, topological groups and topological…
Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we show that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces over \mathbb{R}^{N}…
In this paper, we employ the ABP method developed by Brendle to establish the optimal $L^p$ logarithmic Sobolev inequality on manifolds with nonnegative Ricci curvature, as well as a sharp $L^2$ logarithmic Sobolev inequality for…
This paper is a second one following our work [CLZ13] in series, considering sharp Hardy- Littlewood-Sobolev inequalities on groups of Heisenberg type. The first important breakthrough was made by Frank and Lieb in [FL12]. In this paper,…
Associated to the class of restricted-weak type weights for the Hardy operator, we find a new class of Lorentz spaces for which the normability property holds. This result is analogous to the characterization given by Sawyer for the…
We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds which converge to the true value of the capacity. Several…
We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and their complex and quaternionic…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
In this work, we have proved a version of the Hardy-Littlewood-Sobolev inequality for variable exponents. After we use the variational method to establish the existence of solution for a class of Choquard equations involving the…
We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the $p(\cdot)$-Laplacian type. Our approach is based on the Lewy-Stampacchia inequalities,…