Related papers: $A_p$ weights and Quantitative Estimates in the Sc…

In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse H\"older Inequality for $A_{\infty}$ weights. For two given operators $T$ and $S$, we study $L^p(w)$ bounds of…

Let $L=-\Delta +V$ with non-negative potential $V$ satisfying some appropriate reverse H\"older inequality. In this paper, we study the boundedness of the commutators of some singular integrals associated to $L$ such as Riesz transforms and…

Let $\delta\in(0,n]$, $p\in[1,\infty)$, $\mathcal H_{\infty}^\delta$ denote the Hausdorff content on $\mathbb R^n$, and $\mathcal A_{p,\delta}$ be the capacitary Muckenhoupt weight class. We are interested in understanding the relationship…

Let $\{e^{-tL^{\alpha}}\}_{t>0}$ be the fractional Schr\"{o}dinger semigroup associated with $L=-\Delta+V$, where $V$ is a non-negatvie potential belonging to the reverse H\"{o}lder class. In this paper, we establish weighted boundedness…

The Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p\otimes E}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ twisted by a Hermitian vector bundle $E$ on a Riemannian manifold of bounded geometry is studied. For any…

We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…

We prove $L^{p}$ and weighted $L^{p}$ estimates for bounded functions of a selfadjoint operator satisfying both a pointwise gaussian estimate for its heat kernel and a finite speed of propagation property. As an application, we obtain…

The goal of this note is to establish non-tangential convergence results for Schr\"{o}dinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the…

Let $ \mathcal{L} = -\Delta + V $ be a Schr\"odinger operator acting on $ L^2(\mathbb{R}^n) $, where the nonnegative potential $ V $ belongs to the reverse H\"older class $ RH_q $ for some $ q \geq n/2 $. This article is primarily concerned…

The class $A_\alpha^p$ consists of those analytic functions $f$ in the unit disc such that \[\|f\|_{\alpha,p}^p := |f(0)|^p+\int_0^1 \left(\frac{d}{dr} M_p^p(r,f)\right) (1-r^2)^{\alpha-1} \,dr < \infty,\] where $M_p^p(r,f)$ is the radial…

We prove the sharp mixed $A_{p}-A_{\infty}$ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely \[ \|M\|_{L^{p,q}(w)} \lesssim_{p,q,n}…

This manuscript addresses Muckenhoupt $A_{p}$ weight theory in connection to Morrey and BMO spaces. It is proved that $\omega$ belongs to Muckenhoupt $A_{p}$ class, if and only if Hardy-Littlewood maximal function $M$ is bounded from…

We improve on several weighted inequalities of recent interest by replacing a part of the A_p bounds by weaker A_\infty estimates involving Wilson's A_\infty constant \[ [w]_{A_\infty}':=\sup_Q\frac{1}{w(Q)}\int_Q M(w\chi_Q). \] In…

Let $\mathcal L=-\Delta_{\mathbb H^n}+V$ be a Schr\"odinger operator on the Heisenberg group $\mathbb H^n$, where $\Delta_{\mathbb H^n}$ is the sublaplacian on $\mathbb H^n$ and the nonnegative potential $V$ belongs to the reverse H\"older…

We consider the Schr\"odinger type operator ${\mathcal A}=(1+|x|^{\alpha})\Delta-|x|^{\beta}$, for $\alpha\in [0,2]$ and $\beta\ge 0$. We prove that, for any $p\in (1,\infty)$, the minimal realization of operator ${\mathcal A}$ in…

In this paper, we introduce a Weyl functional calculus $a \mapsto a(Q,P)$ for the position and momentum operators $Q$ and $P$ associated with the Ornstein-Uhlenbeck operator $ L = -\Delta + x\cdot \nabla$, and give a simple criterion for…

Let Omega be a non-empty open proper and connected subset of R^n. Consider p elliptic Schr\"odinger type operator L_{E}u=A_{E}u+V in Omega, and the linear parabolic operator L_{P}u=A_{P}u+Vu in Omega x (0,T), where the coefficients of A_{E}…

This paper constructs a Hardy-Littlewood type maximal operator adapted to the Schr\"{o}dinger operator $\mathcal{L} := -\Delta + |x|^{2}$ acting on $L^{2}(\mathbb{R}^{d})$. It achieves this through the use of the Gaussian grid…

Let $T$ be a non-degenerate Calder\'on-Zygmund operator and let $b:\mathbb{R}^d\to\mathbb{C}$ be locally integrable. Let $1<p\leq q<\infty$ and let $\mu^p\in A_p$ and $\lambda^q\in A_q,$ where $A_{p}$ denotes the usual class of Muckenhoupt…

Part of the intrinsic structure of singular integrals in the Bessel setting is captured by Muckenhoupt-type weights. Anderson--Kerman showed that the Bessel Riesz transform is bounded on weighted $L^p_w$ if and only if $w$ is in the class…