Related papers: On Kato-Sobolev type spaces

In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann…

We define and study homogeneous kinetic Sobolev spaces adapted to the Kolmogorov equation. We consider both local and non-local diffusion. The spaces are built from the Lebesgue spaces L p for all integrability exponents p $\in$ (1,…

In this article we study the family of $BMO^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of…

Let $G$ be a noncompact connected Lie group, denote with $\rho$ a right Haar measure and choose a family of linearly independent left-invariant vector fields $\mathbf{X}$ on $G$ satisfying H\"ormander's condition. Let $\chi$ be a positive…

We introduce a new ladder of function spaces which is shown to fill in the gap between the weak $L^{p\infty}$ spaces and the larger Morrey spaces, $M^p$. Our motivation for introducing these new spaces, denoted $\V^{pq}$, is to gain a more…

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 consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an…

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…

Motivated by the recent characterization of Sobolev spaces due to Brezis-Van Schaftingen-Yung we prove new weak-type inequalities for one parameter families of operators connected with mixed norm inequalities. The novelty here comes from…

We provide an improvement of Calder\'on and Torchinsky's version of the H\"ormander multiplier theorem on Hardy spaces $H^p$ ($0<p<\infty$), by replacing the Sobolev space $L_s^2(A_0)$ by the Lorentz-Sobolev space $L_s^{\tau^{(s,p)}…

We show that a Beurling type theory of invariant subspaces of noncommutative $H^2$ spaces holds true in the setting of subdiagonal subalgebras of $\sigma$-finite von Neumann algebras. This extends earlier work of Blecher and Labuschagne for…

We study harmonic Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$, where $0<p<1$ and $\alpha\in\mathbb{R}$. We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that…

This is a continuation of recent work on the general definition of pseudo-differential operators of type $1,1$, in H\"ormander's sense. Continuity in $L_p$-Sobolev spaces and H\"older--Zygmund spaces, and more generally in Besov and…

We develop the theory for the Bergman spaces of generalized $L_p$-solutions of the bicomplex-Vekua equation $\overline{\boldsymbol{\partial}}W=aW+b\overline{W}$ on bounded domains, where the coefficients $a$ and $b$ are bounded…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…

We show that the Heisenberg Lie algebras over a field $\mathbb{F}$ of characteristic $p>0$ admit a family of restricted Lie algebras, and we classify all such non-isomorphic restricted Lie algebra structures. We use the ordinary 1- and…

We study the weighted compactness and boundedness properties of Toeplitz operators on the Bergman space with respect to B\'ekoll\`e-Bonami type weights. Let $T_u$ denote the Toeplitz operator on the (unweighted) Bergman space of the unit…

We study the well-posedness of Cauchy problems on the upper half space $\mathbb{R}^{n+1}_+$ associated to higher order systems $\partial_t u =(-1)^{m+1}\mbox{div}_m A\nabla ^m u$ with bounded measurable and uniformly elliptic coefficients.…

We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the…