Related papers: Estimates for Brascamp-Lieb forms in $L^p$ spaces …
We define a scale of weighted Morrey spaces which contains different weighted versions appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the…
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 consider convex bodies in $M_{n,m}(\mathbb R)$, the space of matrices of $n$-rows and $m$-columns. A special case of fiber-symmetrization in $M_{n,m}(\mathbb R)$ was recently introduced in [5,6]. We prove a…
In the paper we look for an elegant proof of the characterization of relatively compact families in $L^p-$spaces. At first glance, the suggested approach may seem convoluted and lengthy, but we spare no effort to argue that our proof is in…
By differentiating a concavity principle arising from the Pr\'ekopa-Leindler inequality, we obtain a statement simultaneously strengthening the weighted boundary Poincar\'e inequality and the Brascamp-Lieb variance inequality. The resulting…
Given any (forward) Brascamp--Lieb inequality on euclidean space, a famous theorem of Lieb guarantees that gaussian near-maximizers always exist. Recently, Barthe and Wolff used mass transportation techniques to establish a counterpart to…
We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski…
In this paper, we present a bootstrap procedure for general elliptic systems with $n(\geq 3)$ components. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^\infty$-regularity conditions for the three well-known types of…
We prove that if a weight is a Bekoll\'{e}-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0 < p < \infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic…
We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $\Lambda^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete…
We consider two non-convex formulations for computing the optimal constant in the Brascamp-Lieb inequality corresponding to a given datum, and show that they are geodesically log-concave on the manifold of positive definite matrices endowed…
Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known $1/r$ (Keplerian) and logarithmic…
In this work, we prove a new family of Lieb-Robinson bounds for lattice spin systems with long-range interactions. Our results apply for arbitrary $k$-body interactions, so long as they decay with a power-law greater than $kd$, where $d$ is…
We establish some local and global well-posedness for Hartree-Fock equations of $N$ particles (HFP) with Cauchy data in Lebesgue spaces $L^p \cap L^2 $ for $1\leq p \leq \infty$. Similar results are proven for fractional HFP in…
There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the…
We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted $L^p-L^q$ spaces. As an important example, we investigate transforms with kernel of power type, as for…
We continue our investigation of the intertwining relations for Markov semigroups and extend the results of [9] to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp-Lieb type for…
A new proof is given for the fact that centered gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities, extending the Brascamp-Lieb and Barthe theorems. A duality principle for best constants is also developed,…
We completely characterize the boundedness of the area operators from the Bergman spaces $A^p_\alpha(\mathbb{B}_ n)$ to the Lebesgue spaces $L^q(\mathbb{S}_ n)$ for all $0<p,q<\infty$. For the case $n=1$, some partial results were…
We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions…