Related papers: Multi-parameter singular Radon transforms II: the …

In this paper, we establish the coincidence of two classes of $L^p$-Kato class measures in the framework of symmetric Markov processes admitting upper and lower estimates of heat kernel under mild conditions. One class of $L^p$-Kato class…

In this paper we establish $L^p$ boundedness properties for maximal operators, Littlewood-Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with nonsymmetric Ornstein-Uhlenbeck…

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this paper, we first define molecules for weighted Hardy spaces…

We study boundedness on $L^p(R^d)$ of vertical Littlewood-Paley-Stein functions for Schr\"odinger operators $-\Delta + V$ with nonnegative potential $V$. These functions are proved to be bounded on $L^p$ for all $p \in (1, 2]$. The…

We study singular integral operators induced by Calder\'on-Zygmund kernels in any step-$2$ Carnot group $\mathbb{G}$. We show that if such an operator satisfies some natural cancellation conditions then it is $L^2$ bounded on all intrinsic…

Let $L=-\Delta +|x|^2$ be the Hermite operator on $\mathbb{R}^n$, and $T$ be a Calder\'on-Zygmund type operator that is modelled on certain singular integrals related to $L$. We establish necessary and sufficient conditions for $T$ to be…

The main aim of this article is to establish boundedness of singular integrals with non-smooth kernels on product spaces. Let $L_1$ and $L_2$ be non-negative self-adjoint operators on $L^2(\mathbb{R}^{n_1})$ and $L^2(\mathbb{R}^{n_2})$,…

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…

Given a Calder\'{o}n--Zygmund (C--Z for short) operator $T$, which satisfies H\"ormander condition, we prove that: if $T$ maps all the characteristic atoms to $WL^{1}$, then $T$ is continuous from $L^{p}$ to $L^{p}(1<p<\infty)$. So the…

We prove that the flag kernel singular integral operators of Nagel-Ricci-Stein on a homogeneous group are bounded on the Lp spaces. The gradation associated with the kernels is the natural gradation of the underlying Lie algebra. Our main…

In 2008, J. Parcet showed the $(1,1)$ weak-boundedness of Calder\'on-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools : Cuculescu's projections…

In this paper we study the $L^p$ boundedness of the centred and the uncentred Hardy--Littlewood maximal operators on certain Riemannian manifolds with bounded geometry. Our results complement those of various authors. We show that, under…

The aim of my PhD work is to study the $L^p$-boundedness of operators on two classes of two-step nilpotent Lie groups, using Plancherel formulas and spherical functions as tools. The first class of groups consists of the groups of…

In this work, we provide a complete characterization of the boundedness of two classes of multiparameter Forelli-Rudin type operators from one mixed-norm Lebesgue space $L^{\vec p}$ to another space $L^{\vec q}$, when $1\leq \vec{p}\leq…

This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular…

In this paper, we prove \( L^p \) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \( L^p \) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group…

In this paper we study boundedness and detailed spectral properties for the Ces\`aro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Ces\`aro-Hardy operators and their dual…

We study interior $L^p$-regularity theory, also known as Calderon-Zygmund theory, of the equation \[ \int_{\mathbb{R}^n} \int_{\mathbb{R}^n} \frac{K(x,y)\ (u(x)-u(y))\, (\varphi(x)-\varphi(y))}{|x-y|^{n+2s}}\, dx\, dy = \langle f, \varphi…

In this paper, we show that Hilbert transforms along some curves are bounded on $L^p({\mathbb R}^n;X)$ for some $1<p<\infty$ and some UMD spaces $X$. In particular, we prove that the Hilbert transform along some curves are completely…

Consider the second order divergence form elliptic operator $L$ with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calder\'{o}n-Zygmund theory.…