Related papers: Convolution inequalities for the Boltzmann collisi…
We prove a strong-type interpolation result for noncommutative Orlicz spaces over semifinite von Neumann algebras. Based on this result, we obtain Young-type convolution estimates for the Weyl pseudodifferential symbols of operators in…
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and…
The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…
The main results in the paper are the weighted multipolar Hardy inequalities \begin{equation*} c\int_{\R^N}\sum_{i=1}^n\frac{u^2}{|x-a_i|^2}\,d\mu \leq\int_{\R^N}|\nabla u |^2d\mu+ K\int_{\R^N} u^2d\mu, \end{equation*} in $\R^N$ for any $u$…
We study a regularity property for the gain part of the relativistic Boltzmann collision operator. Our assumptions on the collisional scattering kernel cover the full range of generic hard and soft potentials with angular cut-off.
We consider the Boltzmann operator for mixtures with cutoff Maxwellian, hard potentials, or hard spheres collision kernels. In a perturbative regime around the global Maxwellian equilibrium, the linearized Boltzmann multi-species operator…
We provide a linear analysis on normal modes of the spin Boltzmann equation proposed in \cite{Weickgenannt:2021cuo}, where the non-diagonal or polarized part of the transition rate is neglected to ensure the Hermitian property of linearized…
We apply the spectral-Lagrangian method of Gamba and Tharkabhushanam for solving the homogeneous Boltzmann equation to compute the low probability tails of the velocity distribution function, $f$, of a particle species. This method is based…
In this paper, we obtained the Dunkl analogy of classical Lp Hardy inequality for $p > N + 2\gamma$ with sharp constant $\left(\frac{p-N-2\gamma}{p}\right)^{p}$, where $2\gamma$ is the degree of weight function associated with Dunkl…
We give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of Boltzmann's and Landau's equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing…
In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-P\'{o}lya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^{\beta} ) $ to weighted weak Lebesgue spaces…
Linear interpolation inequalities that combine Hardy's inequality with sharp Sobolev embedding are obtained using classical arguments of Hardy and Littlewood (Bliss lemma). Such results are equivalent to Caffarelli-Kohn-Nirenberg…
This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type $(1,1)$ estimate of noncommutative maximal Calder\'{o}n-Zygmund operators, corresponding…
In this work, we are concerned with the regularities of the solutions to Boltzmann equation with the physical collision kernels for the full range of intermolecular repulsive potentials, $r^{-(p-1)}$ with $p>2$. We give the new and…
In this paper, we investigate weighted composition, Volterra and Integral operators on second derivative Hardy spaces. Some equivalent conditions for boundedness of the operators will be given using the boundedness on the Hardy spaces. Also…
In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms based on…
We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities are bounded and the mass is away from vacuum, we establish…
We present recent results [4, 28, 29] about the quantitative study of the linearized Boltzmann collision operator, and its application to the study of the trend to equilibrium for the spatially homogeneous Boltzmann equation for hard…
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…