Related papers: Inequalities for $\mathrm{BV}^{\mathbb{A}} $-Funct…
In a doubling metric measure space $(X,\rho,\mu)$ supporting a Poincar\'e inequality, we give a new characterisation of first-order Sobolev spaces by mean oscillations, and extend previous characterisations of constant functions in terms of…
In this paper we study several inequalities of log-Sobolev type for Dunkl operators. After proving an equivalent of the classical inequality for the usual Dunkl measure $\mu_k$, we also study a number of inequalities for probability…
If Poincar{\'e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and…
Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…
In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling…
We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincar\'e inequality and are equipped with a doubling measure. The properties we have selected to study are…
In the paper, we consider inequalities of the Poincar\'e--Steklov type for subspaces of $H^1$-functions defined in a bounded domain $\Omega\in \Rd$ with Lipschitz boundary $\partial\Omega$. For scalar valued functions, the subspaces are…
On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first show, using the special topological…
In this paper we introduce conformally covariant boundary operators for Poincar\'e-Einstein manifolds satisfying a mild spectral assumption. Using these boundary operators we set up higher order Dirichlet problems whose solutions are such…
Let $\mu$ and $\nu$ be two probability measures on $\R^d$, where $\mu(\d x)= \e^{-V(x)}\d x$ for some $V\in C^1(\R^d)$. Explicit sufficient conditions on $V$ and $\nu$ are presented such that $\mu*\nu$ satisfies the log-Sobolev, Poincar\'e…
In this paper, we study some functional inequalities (such as Poincar\'e inequalities, logarithmic Sobolev inequalities, generalized Cheeger isoperimetric inequalities, transportation-information inequalities and transportation-entropy…
We prove several Sobolev-type inequalities related to the $\bar\partial$-operator on bounded domains in $\mathbb{C}^n$, which can be viewed as a $\bar\partial$-version of the classical Sobolev inequality and its various generalizations, and…
We investigate the 1D Riemann-Liouville fractional derivative focusing on the connections with fractional Sobolev spaces, the space $BV$ of functions of bounded variation, whose derivatives are not functions but measures and the space…
We study compactness and boundedness of embeddings from Sobolev type spaces on metric spaces into $L^q$ spaces with respect to another measure. The considered Sobolev spaces can be of fractional order and some statements allow also…
We present a class of modified logarithmic Sobolev inequality, interpolating between Poincar\'e and logarithmic Sobolev inequalities, suitable for measures of the type $\exp(-|x|^\al)$ or more complex $\exp(-|x|^\al\log^\beta(2+|x|))$…
We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar\'e inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincar\'e and weak Poincar\'e inequalities was studied in…
We generalize in this article the classical Sobolev's and Sobolev's trace inequalities on the Grand Lebesgue Spaces under monomial weight instead the classical Lebesgue or grand Lebesgue Spaces. We will distinguish the classical Sobolev's…
In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown…
In this paper, we prove capacitary versions of the fractional Sobolev--Poincar\'e inequalities. We characterize localized variant of the boundary fractional Sobolev--Poincar\'e inequalities through uniform fatness condition of the domain in…
We provide new characterizations of Sobolev ad BV spaces in doubling and Poincare metric spaces in the spirit of the Bourgain-Brezis-Mironescu and Nguyen limit formulas holding in domains of R^N.