Related papers: Estimates for differential operators of vector ana…

In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corresponding weighted Sobolev and trace-type inequalities. These…

Sharp affine Hardy--Littlewood--Sobolev inequalities for functions on $\mathbb R^n$ are established, which are significantly stronger than (and directly imply) the sharp Hardy--Littlewood--Sobolev inequalities by Lieb and by Beckner, Dou,…

We prove logarithmic Sobolev inequalities for semi-direct product operators (see definition in Section 1). We apply our main results to examples of operators and provide some applications to ultracontractive bounds of semigroups. Hardy's…

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…

The injectively elliptic vector differential operators $A (\mathrm{D})$ from $V$ to $E$ on $\mathbb{R}^n$ such that the estimate \[ \Vert D^\ell u\Vert_{L^{n/(n - \ell)} (\mathbb{R}^n)} \le \Vert A (\mathrm{D}) u\Vert_{L^1 (\mathbb{R}^n)}…

Via a random construction we establish necessary conditions for $L^p(\ell^q)$ inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported…

We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact…

The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic inequalities, referred to as the chord Sobolev inequalities. A…

We study a family of fractional integral operators defined on Heisenberg groups. The kernels of these operators satisfy Zygmund dilations. We obtain a Hardy-Littlewood-Sobolev type inequality.

The previous "Polynomial Capacities, Poincare' type inequalities and Spectral synthesis in Sobolev space" is a prerequisite. A parallell reading is recommended.

We study in this article a new pointwise estimate for ''rough'' singular integral operators. From this pointwise estimate we will derive Sobolev type inequalities in a variety of functional spaces.

We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants. The contents: 1. Estimate for a quadratic form of…

The L 1-Sobolev inequality states that the L n/(n--1)-norm of a compactly supported function on Euclidean n-space is controlled by the L 1-norm of its gradient. The generalization to differential forms (due to Lanzani & Stein and Bourgain &…

Upper and lower estimates are obtained for the Schatten-von Neumann norms of the Hardy-Steklov operator in Lebesgue function spaces on the semi-axis.

This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group $\mathbb{H}^n$. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and…

We prove a family of Sobolev inequalities of the form $$ \Vert u \Vert_{L^{\frac{n}{n-1}, 1} (\mathbb{R}^n,V)} \le \Vert A (D) u \Vert_{L^1 (\mathbb{R}^n,E)} $$ where $A (D) : C^\infty_c (\mathbb{R}^n, V) \to C^\infty_c (\mathbb{R}^n, E)$…

We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators of order zero. Sharp remainder terms of $L^{p}$ and weighted Sobolev type and…

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…

Our main goal is to investigate supercritical Hardy-Sobolev type inequalities with a logarithmic term and their corresponding variational problem. We prove the existence of extremal functions for the associated variational problem, despite…

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…