相关论文: Quantitative Weighted Estimates for Schr\"odinger …

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 study Fourier multipliers on noncommutative spaces. In particluar, we show a simple proof of $L^p$-$L^q$ estimate of Fourier multipliers on general noncommutative spaces associated with semi-finite von Neumann algebras.…

We study eigenvalues of non-self-adjoint Schr\"odinger operators on non-trapping asymptotically conic manifolds of dimension $n\ge 3$. Specifically, we are concerned with the following two types of estimates. The first one deals with Keller…

As our main result, we supply the missing characterization of the $L^p(\mu)\to L^q(\lambda)$ boundedness of the commutator of a non-degenerate Calder\'on--Zygmund operator $T$ and pointwise multiplication by $b$ for exponents $1<q<p<\infty$…

We present a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors. We apply our formula to the particular case of interpolation of matrix weighted $L^p$ spaces by the real and complex…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

In this work sufficient conditions on the order of the symbol are developed to ensure boundedness, compactness and r-nuclearity of pseudo-differential operators in $\hbar\mathbb{Z}^n$. In addition, these conditions allow us to obtain growth…

In this paper, we first introduce the new class of multiple weights $A^\vc_{\vec{p}}$ which is larger than the class of multiple weights in \cite{LOPTG}. Then, using this class of weights, we study the weighted norm inequalities for certain…

In this paper we establish the $L^p$-$L^q$ estimates for global pseudo-differential operators on graded Lie groups. We provide both necessary and sufficient conditions for the $L^p$-$L^q$ boundedness of pseudo-differential operators…

In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal…

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}…

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…

We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…

We consider weighted operators acting on $L^p(\mathbb{R}^d)$ and show that they depend continuously on the weight $w\in A_p(\mathbb{R}^d)$ in the operator topology. Then, we use this result to estimate $L^p_w(\mathbb{T})$ norm of…

We present a new criterion for the weighted $L^p-L^q$ boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates…

Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the wave…

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.

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…

We consider a conjecture attributed to Muckenhoupt and Wheeden which suggests a positive relationship between the continuity of the Hardy-Littlewood maximal operator and the Hilbert transform in the weighted setting. Although continuity of…

In this paper, we establish the boundedness of the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belong to both Lipschitz space and central…