Commutator estimates in $W^{*}$-factors

Lipschitz Estimates for Multilinear Commutator of Pseudo-differential Operators

As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [4, 5, 6, 7, 8, 9, 10]). In [4, 5, 6, 7, 8, 9, 10], the authors prove that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on L(R) for 1 < p <∞; Chanillo (see [2]) proves a similar result when singular int...

AUni¢ed Theoryof Commutator Estimates fora Class of Interpolation Methods

Lipschitz Estimates for Multilinear Commutator of Littlewood-paley Operator

Let T be the Calderón-Zygmund operator, Coifman, Rochberg and Weiss (see [4]) proves that the commutator [b, T ](f) = bT (f) − T (bf)(where b ∈ BMO(R)) is bounded on L(R) for 1 < p <∞. Chanillo (see [2]) proves a similar result when T is replaced by the fractional operators. In [8, 16], Janson and Paluszynski study these results for the Triebel-Lizorkin spaces and the case b ∈ Lipβ(R), where Li...

Lp Spectral Independence of Elliptic Operators via Commutator Estimates

Let fT p : q 1 p q 2 g be a family of consistent C 0 semigroups on L p ((), with q 1 ; q 2 2 1; 1) and R n open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p 2 q 1 ; q 2 ]. Applications include the case of Petrovskij correct systems with HH older continuous coeecients, Schrr odinger operators, ...

W Estimates for the Monge-ampère Equation

We study strictly convex Alexandrov solutions u of the real MongeAmpère equation det(∇2u) = f , where f is measurable, positive, and bounded away from 0 and ∞. Under only these assumptions we prove interior Wregularity of u.