Related papers: The Sharp Log-Sobolev Inequality on a Compact Inte…

This paper studies the existence of extremal problems for the Hardy-Littlewood-Sobolev inequalities on compact manifolds without boundary via Concentration-Compactness principle.

Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. The estimates are uniform with respect to all graphs of a given finite length, and the constant factors in the…

This paper deals with a class of Sobolev spaces of vector-valued functions on a compact group. Some Sobolev embedding theorems are proved.

A family of sharp $L^p$ Sobolev inequalities is established by averaging the length of $i$-dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical $L^p$…

We prove the classical Hausdorff-Young inequality for Orlicz spaces on compact homogeneous manifolds.

We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.

We study higher complex Sobolev spaces and their corresponding functional capacities. In particular, we prove the Moser-Trudinger inequality for these spaces and discuss some relationships between these spaces and the complex…

In this short paper, we establish a range of Caffarelli-Kohn-Nirenberg and weighted $L^{p}$-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev…

In this article, we determine the Rogosinski radii for certain subclasses of close-to-convex functions defined on open unit disc $\mathbb{D}= \{z \in \mathbb{C}: |z| < 1\}$. Furthermore, we establish improved versions of the classical Bohr…

We study quantitative stability results for different classes of Sobolev inequalities on general compact Riemannian manifolds. We prove that, up to constants depending on the manifold, a function that nearly saturates a critical Sobolev…

The goal of this short note is to prove qualitative stability for a family of trace Sobolev inequalities first proven by Carlen \& Loss for $p=2$ and by Maggi and the author for $p\in (1,n)$. This answers an open problem raised in a recent…

We show that the convolution of a compactly supported measure on $\mathbb{R}$ with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). We use this result to give a new proof of a classical result in random matrix theory…

Our main goal is to explicitly compute the best constant for the Sobolev-type inequality involving the polyharmonic operator obtained in (Analysis and Applications 22, pp. 1417-1446, 2024). To achieve this goal, we also establish both…

A sharp lower bound for the first Dirichlet eigenvalue of the $p$-laplacian in Gaussian space is derived for sets with prescribed generalized torsional rigidity. The result provides an extension of the classical spectral inequality due to…

We prove fractional Hardy--Sobolev--Maz'ya inequality for balls and a half-space, partially answering the open problem posed by Frank and Seiringer [arXiv:0906.1561v1 [math.FA], 2009] We note that for half-spaces this inequality has been…

The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or…

We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski…

In this paper we show a number of logarithmic inequalities on several classes of Lie groups: log-Sobolev inequalities on general Lie groups, log-Sobolev (weighted and unweighted), log-Gagliardo-Nirenberg and log-Caffarelli-Kohn-Nirenberg…

We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with $\alpha$-homogeneous potential $V$ is equivalent to a $p$-Brunn--Minkowski inequality for level sets of $V$ with some $p(\alpha,n)<0$. We…

We consider the Hardy-Littlewood-Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices $\vec p$ and $\vec q$ such that the Riesz potential is bounded from $L^{\vec p}$ to $L^{\vec q}$, including…