相关论文: Maximal Inequalities and Riesz Transform Estimates…

The paper concerns the magnetic Schr\"odinger operator on $R^n$. We prove some $L^p$ estimates on the Riesz transforms and we establish some related maximal inequalities. The conditions that we arrive at, are essentially based on the…

We consider vector-valued magnetic Schr\"odinger operators $-\bm \Delta_{\bm a}+V$ with magnetic potential $\bm a \in L^2_{\mathrm{loc}}(\mathbb{R}^d;\mathbb{R}^d)$ and electric potential $V$ given by a matrix-valued function whose entries…

We show various $L^p$ estimates for Schr\"odinger operators $-\Delta+V$ on $\RR^n$ and their square roots. We assume reverse H\"older estimates on the potential, and improve some results of Shen \cite{Sh1}. Our main tools are improved…

We prove $L^p$ and smoothing estimates for the resolvent of magnetic Schr\"odinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we…

We obtain $L^p$ estimates of the maximal Schr\"odinger operator in $\mathbb R^n$ using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.

As it was shown by Shen, the Riesz transforms associated to the Schr\"odinger operator $L=-\Delta + V$ are not bounded on $L^p(\mathbb{R}^d)$-spaces for all $p, 1<p<\infty$, under the only assumption that the potential satisfies a reverse…

Let $M=(0,\infty)_r\times Y$ be a $d$-dimensional ($d\ge 3$) metric cone with metric<br/>$g=dr^2+r^2h$, where $(Y,h)$ is a closed Riemannian manifold. Let<br/>$H=\Delta+V_0/r^2$ be the associated Schrodinger operator, with<br/>$V_0\in…

We establish various $L^{p}$ estimates for the Schr\"odinger operator $-\Delta+V$ on Riemannian manifolds satisfying the doubling property and a Poincar\'e inequality, where $\Delta $ is the Laplace-Beltrami operator and $V$ belongs to a…

In this work we obtain weighted $L^p$, $1<p<\infty$, and weak $L\log L$ estimates for the commutator of the Riesz transforms associated to a Schr\"odinger operator $-\lap+V$, where $V$ satisfies some reverse H\"older inequality. The classes…

We study the boundedness of Riesz transforms in $L^p$ for $p>2$ on a doubling metric measure space endowed with a gradient operator and an injective, $\omega$-accretive operator $L$ satisfying Davies-Gaffney estimates. If $L$ is…

We prove magnetic interpolation inequalities and Keller-Lieb-Thir-ring estimates for the principal eigenvalue of magnetic Schr{\"o}dinger operators. We establish explicit upper and lower bounds for the best constants and show by numerical…

In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson--Landau-type inequalities and to magnetic Schrodinger operators. We also obtain…

In this paper we consider the vector-valued Schr\"{o}dinger operator $-\Delta + V$, where the potential term $V$ is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb{R}^d)$ and, for every $x\in\mathbb{R}^d$, $V(x)$ is…

We consider Schroedinger operators on metric cones whose cross section is a closed Riemannian manifold $(Y, h)$ of dimension $d-1 \geq 2$. Thus the metric on the cone $M = (0, \infty)_r \times Y$ is $dr^2 + r^2 h$. Let $\Delta$ be the…

Let Lf(x)=-\Delta f(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a non-negative self-adjoint Schr\"odinger operator on R^d. We say that an L^1-function f belongs to the Hardy space H^1_L if the maximal function M_L f(x)=\sup_{t>0}…

We prove optimal Lieb-Thirring type inequalities for Schr\"odinger and Jacobi operators with complex potentials. Our results bound eigenvalue power sums (Riesz means) by the $L^p$ norm of the potential, where in contrast to the self-adjoint…

In this paper we prove Lieb--Thirring inequalities for magnetic Schr\"odinger operators on the torus, where the constants in the inequalities depend on the magnetic flux.

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schr\"odinger Calder\'on-Zygmund operators of $(s,\delta)$ type, for $1<s\leq \infty$ and $0<\delta \leq 1$. We also give estimates of…

We prove sharp Lieb-Thirring inequalities for Schroedinger operators with potentials supported on a hyperplane and we show how these estimates are related to Lieb-Thirring inequalities for relativistic Schroedinger operators.

In this paper, we obtain the desired noncommutative maximal inequalities of the truncated Calder\'on-Zygmund operators of non-convolution type acting on operator-valued $L_p$-functions for all $1<p<\infty$, answering a question left open in…