Related papers: Some functional inequalities on polynomial volume …
We prove a scale of generalized $L^p$-Poincar\'e inequalities and Sobolev type inequalities on graphs with polynomial volume growth. They are optimal on Vicsek graphs.
We introduce a Littlewood-Paley decomposition related to any sub-Laplacian on a Lie group G of polynomial volume growth; this allows us to prove a Littlewood-Paley theorem in this general setting and to provide a dyadic characterization of…
We study in this article the Improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms…
We develop characterizations for Sobolev spaces of potential type on graded Lie groups, by means of Littlewood-Paley square functions, and Strichartz functionals involving second-order differences. A key role is played by some mean value…
In this paper, we uncover a novel connection between the Fenchel-Willmore inequality and a new logarithmic Sobolev inequality for mean-convex submanifolds immersed in non-negatively curved manifolds with Euclidean volume growth. Building on…
The article proves an assertion analogous to the Littlewood-Paley theorem for the orthoprojectors onto mutually orthogonal subspaces of piecewise polynomial functions on the cube $ I^d. $ This assertion provides an upper estimate for the…
The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +$\infty$. In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. When p > 1, using as base space classical Lorentz spaces…
In this paper, we show a parabolic version of the Ogawa type inequality in Sobolev spaces. Our inequality provides an estimate of the $L^{\infty}$ norm of a function in terms of its parabolic $BMO$ norm, with the aid of the square root of…
Let $P_1, \ldots, P_m \in K[y]$ be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field $K$. We give a quantitative count of the number of polynomial progressions $x, x+P_1(y),…
In this paper a Pohozaev type inequality is stated for variable exponent Sobolev spaces in order to prove non existence of nontrivial weak solutions for a Dirichlet problem with non-standard growth. The obtained results generalize a…
We provide a family of global weighted Sobolev inequalities and Hardy inequalities on PI spaces with possibly non-maximal volume growth. Our results apply notably to non-trivial Ahlfors regular spaces like Laakso spaces and Kleiner-Schioppa…
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…
We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to the case of H-type groups, this algebra property is generalized to paraproduct…
This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type…
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…
We derive some anisotropic Sobolev inequalities in $\mathbb{R}^{n}$ with a monomial weight in the general setting of rearrangement invariant spaces. Our starting point is to obtain an integral oscillation inequality in multiplicative form.
Let $G$ be a real connected Lie group with polynomial volume growth, endowed with its Haar measure $dx$. Given a $C^2$ positive function $M$ on $G$, we give a sufficient condition for an $L^2$ Poincar\'e inequality with respect to the…
We prove a sharp Log-Sobolev inequality for submanifolds of a complete non-compact Riemannian manifold with asymptotic non-negative intermediate Ricci curvature and Euclidean volume growth. Our work extends a result of Dong-Lin-Lu which…
Introduced by Gromov in the nineties, the systolic growth of a Lie group gives the smallest possible covolume of a lattice with a given systole. In a simply connected nilpotent Lie group, this function has polynomial growth, but can grow…
We establish sharp Sobolev embedding properties within a broad class of compact matrix quantum groups of Kac type under the polynomial growth or the rapid decay property of their duals. Main examples are duals of polynomially growing…