Weighted norm inequalities for potential operators

Weighted Norm Inequalities for Fractional Operators

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels. Indiana Univ. Ma...

Weighted norm inequalities for singular integral operators

On Some Weighted Norm Inequalities for Littlewood–paley Operators

It is shown that the Lw,1< p<∞, operator norms of Littlewood–Paley operators are bounded by a multiple of ‖w‖ Ap , where γp = max{1, p/2} 1 p−1 . This improves previously known bounds for all p > 2. As a corollary, a new estimate in terms of ‖w‖Ap is obtained for the class of Calderón–Zygmund singular integrals commuting with dilations.

On Weighted Norm Inequalities for Positive Linear Operators

Let T be a positive linear operator defined for nonnegative functions on a rj-finite measure space {X,m,fi). Given 1 < p < oo and a nonnegative weight function w on X , it is shown that there exists a nonnegative weight function v , finite /¿-almost everywhere on X , such that (1) I \Tf)*wdfi< j fvd/i, for all/>0, J x J x tere exists posi ( h if and only if th tive /¿-almost everywhere on X...

Weighted Norm Inequalities for Pseudo-pseudodifferential Operators Defined by Amplitudes

We prove weighted norm inequalities for pseudodifferential operators with amplitudes which are only measurable in the spatial variables. The result is sharp, even for smooth amplitudes. Nevertheless, in the case when the amplitude contains the oscillatory factor ξ 7→ ei|ξ| , the result can be substantially improved. We extend the Lpboundedness of pseudo-pseudodifferential operators to certain w...