Related papers: Littlewood-Paley-Stein functionals: an R-boundedne…

In this paper we prove that the Hardy-Littlewood maximal operator is bounded on Morrey spaces $\mathcal{M}_{1,\lambda}(\rn)$, $0 \le \la < n$ for radial, decreasing functions on $\rn$

We prove the boundedness of the non-local operator \[ \mathcal{L}^a u(x)=\int_{\mathbb{R}^d} \left(u(x+y)-u(x)-\chi_\alpha(y)\big(\nabla u(x),y\big)\right) a(x,y)\frac{dy}{|y|^{d+\alpha}} \] from $H_{p,w}^\alpha(\mathbb{R}^d)$ to…

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schr\"odinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical…

Let $X$ be a space of homogeneous type. Assume that $L$ is an non-negative second-order self-adjoint operator on $L^2\left(X\right)$ with (heart) kernel associated to the semigroup $e^{ - tL}$ that satisfies the Gaussian upper bound. In…

The purpose of this paper is to prove pointwise inequalities and to establish the boundedness on weighted $L^{p}$ spaces for pseudo-differential operators $T_{a}$ defined by the symbol $a\in S^{m}_{\varrho,\delta}$ with $0\leq\varrho\leq1,$…

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…

The purpose of this paper is to study the $L^p$ boundedness of operators of the form \[ f\mapsto \psi(x) \int f(\gamma_t(x))K(t)\: dt, \] where $\gamma_t(x)$ is a $C^\infty$ function defined on a neighborhood of the origin in $(t,x)\in…

In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\infty$, we look for operators $\mathcal{M}$ such that the inequality $$\int |Tf|^pw\leq C\int |f|^p…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$ and $H_X({\mathbb R}^n)$ the Hardy space associated with $X$, and let $\alpha\in(0,n)$ and $\beta\in(1,\infty)$. In this article, assuming that the (powered) Hardy--Littlewood…

We consider the higher order Schr\"odinger operator $H=(-\Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\in \mathbb N$, $m>1$. When $n$ is odd, we prove that the wave operators extend to bounded operators on…

Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\RR^n \setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz…

Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this paper,…

We consider the Hodge Laplacian $\Delta$ on the Heisenberg group $H_n$, endowed with a left-invariant and U(n)-invariant Riemannian metric. For $0\le k\le 2n+1$, let $\Delta_k$ denote the Hodge Laplacian restricted to $k$-forms. Our first…

We consider self-adjoint semigroups $T_t = \exp(-tA)$ acting on $L^2(\Omega)$ and satisfying (generalised) Gaussian estimates, where $\Omega$ is a metric measure space of homogeneous type of dimension $d$. The aim of the article is to show…

In this paper, we provide the boundedness property of the Riesz transforms associated to the Schr\"odinger operator $\mathcal{L}=-\Delta + \mathbf{V}$ in a new weighted Morrey space which is the generalized version of many previous Morrey…

In this article, the authors consider the Schr\"{o}dinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative potential…

We show, by applying discrete weighted norm inequalities and the Rubio de Francia algorithm, that the discrete Hilbert transform and discrete Riesz potential are bounded on variable $\ell^{p(\cdot)}(\mathbb{Z})$ spaces whenever the discrete…

Let $H = \Delta^2 + V$ be the fourth-order Schr\"odinger operator on $\mathbb{R}^3$ with a real-valued fast-decaying potential $V$. If zero is neither a resonance nor an eigenvalue of $H$, then it was recently shown that the wave operators…

Let $X$ be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of $H_X(\mathbb{R}^n)$, the Hardy space associated with $X$, via the Littlewood--Paley…

In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-P\'{o}lya-type integral operators acting on $p$-adic weighted Lebesgue spaces. We completely characterize $L^{q}-L^{r}$ boundedness of…