相关论文: Weighted norm inequalities for pseudo-differential…

This paper is dedicated to study weighted $L^p$ inequalities for pseudo-differential operators with amplitudes and their commutators by using the new class of weights $A_p^\vc$ and the new BMO function space BMO$_\vc$ which are larger than…

We establish general weighted $L^2$ inequalities for pseudodifferential operators associated to the H\"ormander symbol classes $S^m_{\rho,\delta}$. Such inequalities allow to control these operators by fractional "non-tangential" maximal…

In the present work we give a simple method to obtain weighted norm inequalities in Lebesgue spaces $L_{p,\gamma }$ with Muckenhoupt weights $\gamma $. This method is different from celebrated Extrapolation or Interpolation Theory. In this…

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 $0\leq\varrho\leq1,$…

In this work, we develop $L^p$ boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the $x$ variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in terms of scale…

In this article, we investigate the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schr\"odinger operators. The weight classes we consider are tailored to this framework and strictly contain the…

We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted $L^p$ spaces over $\mathbb{R}^d$ with weights of the form $\exp(-\phi(x))$, for $\phi$ a $C^2$ function, a setting in which the…

In this paper, we study elements of symbolic calculus for pseudo-differential operators associated with the weighted symbol class $M_{\rho, \Lambda}^m(\mathbb{ T}\times \mathbb{Z})$ (associated to a suitable weight function $\Lambda$ on…

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…

We prove weighted strong $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators. For the first family of operators the weights used can be either Sawyer's one-sided $A^+_p$ weights or Muckenhoupt's…

In this paper, we study the $M$-ellipticity of Fredholm pseudo-differential operators associated with weighted symbols on $L^p(\mathbb{R}^n)$, $1 < p < \infty$. We also prove the G\r{a}rding's inequality for $M$-elliptic operators and the…

Given a compact Lie group $G$, in this paper we establish $L^p$-bounds for pseudo-differential operators in $L^p(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the non-commutative analogue of the phase…

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…

Variable Muckenhoupt weights are considered in variable exponent Lebesgue spaces. Applications are given for polynomial approximation in these spaces. Boundedness of averaging operator is proved to gain a transference result. Almost all…

This is the first part of a series of three articles. In this paper, we obtain weighted norm inequalities for different conical square functions associated with the Heat and the Poisson semigroups generated by a second order divergence form…

In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates.

We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$ is not infinitely smooth with respect to $x$. Decomposing such symbols into four -sometimes five- components and using tools of paradifferential calculus, we derive…

We study two weight norm inequalities for a vector-valued operator from a weighted $L^p(\sigma)$-space to mixed norm $L^q_{l^s}(\mu)$ spaces, $1<q<p$. We apply these results to the boundedness of Wolff's potentials.

This paper finishes the goal of the authors started in two previous manuscripts dedicated to revisiting the continuity properties of toroidal pseudo-differential operators with symbols in the H\"ormander classes. Here we prove pointwise…

Let $\mathcal{L}$ be a Schr\"{o}dinger operator and $\mathcal{V}_\varrho(e^{-t\mathcal{L}})$ be the variation operator of heat semigroup associated to $\mathcal{L}$ with $\varrho>2$. In this paper, we first obtain the quantitative weighted…