Related papers: Estimates for differential operators of vector ana…
We study a family of fractional integral operators defined in $\mathbb{R}^3$ whose kernels are distributions associated with Zygmund dilations: $(x_1, x_2, x_3) \rightarrow (\delta_1 x_1, \delta_2 x_2, \delta_1\delta_2 x_3)$ for…
We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on R^n in terms of their L^1 norm.
In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…
A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the…
We prove a trace Hardy type inequality with the best constant on the polyhedral convex cones which generalizes recent results of Alvino et al. and of Tzirakis on the upper half space. We also prove some trace Hardy-Sobolev-Maz'ya type…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive…
In this paper, we prove trace-type Poincar\'e and Sobolev inequalities for the space of functions of bounded $\mathbb{A}$-Variation
We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained…
In this paper we describe the Euler semigroup $\{e^{-t\mathbb{E}^{*}\mathbb{E}}\}_{t>0}$ on homogeneous Lie groups, which allows us to obtain various types of the Hardy-Sobolev and Gagliardo-Nirenberg type inequalities for the Euler…
We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.
In this paper, we study the existence of extremal functions of the discrete Sobolev inequality and Hardy-Littlewood-Sobolev inequality on lattice graphs. We introduce the discrete Concentration-Compactness principle, and prove the existence…
The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type…
We prove that in the context of general Markov semigroups Beckner inequalities with constants separated from zero as $p\to 1^+$ are equivalent to the modified log Sobolev inequality (previously only one implication was known to hold in this…
New Hardy type inequality with double singular kernel and with additional logarithmic term in a ball $B\subset \mathbb{R}^n$ is proved. As an application an estimate from below of the first eigenvalue for Dirichlet problem of p-Laplacian in…
We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not…
Shifted variants of (dyadic) Hardy-Littlewood maximal function and Stein's square function have played a significant role in the study of many important operators such as Calderon commutators, (bilinear) Hilbert transforms, multilinear…
This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional…
In this paper we study Hardy and Rellich type inequalities for Baouendi-Grushin vector fields : $\nabla_{\gamma}=(\nabla_x, |x|^{2\gamma}\nabla_y)$ where $\gamma>0$, $\nabla_x$ and $\nabla_y$ are usual gradient operators in the variables…