Related papers: Hardy-Sobolev interpolation inequalities
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case $p=n\geq2.$ In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the…
In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…
Four Jacobi settings are considered in the context of Hardy's inequality: the trigonometric polynomials and functions, and the corresponding symmetrized systems. In the polynomial cases sharp Hardy's inequality is proved for the type…
We prove an improved version of Poincar\'e-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Hardy type inequality with an improved constant (than the…
We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.
The paper deals with natural generalizations of the Hardy-Sobolev-Maz'ya inequality and some related questions, such as the optimality and stability of such inequalities, the existence of minimizers of the associated variational problem,…
We study the Hardy inequality when the singularity is placed on the boundary of a bounded domain in $\mathbb{R}^n$ that satisfies both an interior and exterior ball condition at the singularity. We obtain the sharp Hardy constant $n^2/4$ in…
We study a family of fractional integral operator defined on an homogeneous space with a "rectangle doubling" measure. As a result, we give an extension of the classical Hardy-Littlewood-Sobolev theorem to a multi-parameter setting.
In this paper we propose a unified approach, based on limiting interpolation, to investigate the embeddings for the Sobolev space $(\dot{W}^k_p(\mathcal{X}))_0, \, \mathcal{X} \in \{\mathbb{R}^d, \mathbb{T}^d, \Omega\}$, in the subcritical…
This paper studies the existence of extremal problems for the Hardy-Littlewood-Sobolev inequalities on compact manifolds without boundary via Concentration-Compactness principle.
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…
In a previous paper we developed a new method to obtain symmetrization inequalities of Sobolev type for functions in $W_{0}^{1,1}(\Omega)$. In this paper we extend our method to Sobolev functions that do not vanish at the boundary.
We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.…
In this article we compute the best Sobolev constants for various Hardy-Sobolev inequalities with sharp Hardy term. This is carried out in three different environments: interior point singularity in Euclidean space, interior point…
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 give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…
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…
In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr\"odinger equation in all dimensions based on the recent linear profile decomposition results. We then present a new proof…
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…
We study sharp weighted Sobolev-type inequalities of the form \[ \int_{0}^{1}|u(x)|\rho(x) \diff x \leqslant \Lambda \Bigl(\int_{0}^{1}|u^{(k)}(x)|^2 \diff x\Bigr)^{1/2}, \qquad u\in H_0^k(0,1), \] where $\rho$ is a non-negative weight. We…