Related papers: A note on Poincar\'e-Sobolev type inequalities on …

We continue the $U$-bound program initiated in [J. Funct. Anal. 258, 814-851 (2010)] and prove super-Poincar\'e inequalities for a class of subelliptic probability measures defined on M\'etivier groups, the main ingredient in the proof…

We present an argument which leads from the Brunn-Minkowski inequality to a Poincare' type inequality on the boundary of convex bodies with smooth boundary and positive Gauss curvature

In this paper, we consider a new weak norm, iterated weak norm in Lebesgue spaces with mixed norms. We study properties of the mixed weak norm and the iterated weak norm and present the relationship between the two weak norms. Even for the…

We investigate the density of compactly supported smooth functions in the Sobolev space $W^{k,p}$ on complete Riemannian manifolds. In the first part of the paper, we extend to the full range $p\in [1,2]$ the most general results known in…

We prove an equivalence between weighted Poincare inequalities and the existence of weak solutions to a Neumann problem related to a degenerate p- Laplacian. The Poincare inequalities are formulated in the context of degenerate Sobolev…

We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev and Besov norms in $L_{p}$-spaces on smooth compact Riemannian manifolds. For compact homogeneous manifolds, we establish estimates which…

In this paper, inspired by [4, 9], we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry-\'Emery Ricci curvature.

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular…

We define abstract Sobolev type spaces on $\mathsf{L}^p$-scales, $p\in [1,\infty)$, on Hermitian vector bundles over possibly noncompact manifolds, which are induced by smooth measures and families $\mathfrak{P}$ of linear partial…

We consider the spaces $L^p(X,\nu;V)$, where $X$ is a separable Banach space, $\mu$ is a centred non-degenerate Gaussian measure, $\nu:=Ke^{-U}\mu$ with normalizing factor $K$ and $V$ is a separable Hilbert space. In this paper we prove a…

In the paper we pursue the analysis from the section 5 of the Talagrand's paper "Sample boundedness of stochastic processes under increment conditions." Ann. Probab. 18, No. 1, 1-49. In particular we give the proof of some Sobolev…

Sobolev-type inequalities have been extensively studied in the frameworks of real-valued functions and non-commutative $\mathbb{L}_p$ spaces, and have proven useful in bounding the time evolution of classical/quantum Markov processes, among…

In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type $\mathbb{X}=U/K$, of rank $1$ and $2$, the Sobolev regularity threshold $\alpha >1/2$ for the initial data, is sufficient…

We consider several local versions of the doubling condition and Poincar\'e inequalities on metric spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding…

An embedding theorem for Sobolev spaces built upon general Musielak-Orlicz norms is offered. These norms are defined in terms of generalized Young functions which also depend on the $x$ variable. Under minimal conditions on the latter…

We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.

We prove second and fourth order improved Poincar\'e type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as…

The classical Poincar\'e inequality establishes that for any bounded regular domain $\Omega\subset \R^N$ there exists a constant $C=C(\Omega)>0$ such that $$ \int_{\Omega} |u|^2\, dx \leq C \int_{\Omega} |\nabla u|^2\, dx \ \ \forall u \in…

In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of…

In this work, we establish a local smoothing result on metrics with small curvature concentration with respect to Sobolev constants and volume growth. In contrast with all previous works, we remove the Ricci curvature condition and…