Weighted inequalities for commutators of Schr\"odinger-Riesz transforms

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 of weights as well as the classes of symbols are larger than $A_p$ and $BMO$ corresponding to the classical Riesz transforms

Weighted inequalities for negative powers of Schrödinger operators

AbstractIn this article we obtain boundedness of the operator (−Δ+V)−α/2 from Lp,∞(w) into weighted bounded mean oscillation type spaces BMOLβ(w) under appropriate conditions on the weight w. We also show that these weighted spaces also have a point-wise description for 0<β<1. Finally, we study the behaviour of the operator (−Δ+V)−α/2 when acting on BMOLβ(w)

Relations between weighted Orlicz and BMOϕBMO_\phi spaces through fractional integrals

summary:We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator $I_\alpha$ maps weak weighted Orlicz$-\phi$ spaces into appropriate weighted versions of the spaces $BMO_\psi$, where $\psi (t)=t^{\alpha /n}\phi ^{-1}(1/t)$. This generalizes known results about boundedness of $I_\alpha$ from weak $L^p$ into Lipschitz spaces for $p>n/\alpha$ and from weak $L^{n/\alpha }$ into $BMO$. It turns out that the class of weights corresponding to $I_\alpha$ acting on weak$-L_\phi$ for $\phi$ of lower type equal or greater than $n/\alpha$, is the same as the one solving the problem for weak$-L^p$ with $p$ the lower index of Orlicz-Maligranda of $\phi$, namely $\omega ^{p'}$ belongs to the $A_1$ class of Muckenhoupt

Whitney coverings and the tent spaces T1,q(γ)T^{1,q}(\gamma) for the Gaussian measure

We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1,q}$ of Coifman, Meyer and Stein.Comment: 13 pages, 1 figure. Revised version incorporating referee's comments. To appear in Arkiv for Matemati

Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\infty})-functional calculus on these spaces. This provides a new way of proving functional calculus of (A) on the Bochner spaces (L^p(\R^n;X)) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when (X=\C), our approach gives refined (p)-dependent versions of known results.Comment: 28 pages; submitted for publicatio