Endpoint Estimates for Commutators of Singular Integral Operators (original) (raw)

Sharp weighted endpoint estimates for commutators of singular integrals

Michigan Mathematical Journal, 2001

The main purpose of this paper is to improve the main result in [P2] by means of a direct proof that avoids the classical good-λ technique considered there. The good-λ method, introduced by of D. Burkholder and R. Gundy in [BG], is a powerful tool but has the disadvantage that it is essentially adapted to measures satisfying the A ∞ condition such as the Lebesgue measure. The approach we consider here is more related to the classical argument of Calderón and Zygmund for proving that singular integral operators satisfy the weak type (1, 1) property having the advantage that it allows to consider more general measure. The method, however, must be different since commutators of singular integral operators with BM O functions are not of weak type (1, 1) as shown in [P2].

Sharp weighted endpoint estimates for com-mutators of singular integral operators

2001

The main purpose of this paper is to improve the main result in [P2] by means of a direct proof that avoids the classical good-λ technique considered there. The good-λ method, introduced by of D. Burkholder and R. Gundy in [BG], is a powerful tool but has the disadvantage that it is essentially adapted to measures satisfying the A ∞ condition such as the Lebesgue measure. The approach we consider here is more related to the classical argument of Calderón and Zygmund for proving that singular integral operators satisfy the weak type (1, 1) property having the advantage that it allows to consider more general measure. The method, however, must be different since commutators of singular integral operators with BM O functions are not of weak type (1, 1) as shown in [P2].

End-point estimates for iterated commutators of multilinear singular integrals

arXiv preprint arXiv: …, 2010

Iterated commutators of multilinear Calderón-Zygmund operators and pointwise multiplication with functions in BM O are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted results involving the vectors weights of the multilinear Calderón-Zygmund theory recently introduced in the literature. Some better than expected estimates for certain multilinear operators are presented too.

On commutators of singular integrals and bilinear singular integrals

Transactions of the American Mathematical Society, 1975

Lp estimates for multilinear singular integrals generalizing Calderón's commutator integral are obtained. The methods introduced involve Fourier and Mellin analysis. 1. In this paper we introduce new methods to obtain estimates for commutators of singular integrals as well as other related operators.

End-points estimates for iterated commutators of multilinear singular integrals

2016

Iterated commutators of multilinear Calderón-Zygmund operators and pointwise multiplication with functions in BM O are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted results involving the vectors weights of the multilinear Calderón-Zygmund theory recently introduced in the literature. Some better than expected estimates for certain multilinear operators are presented too.

Sharp weighted estimates for vector-valued singular integral operators and commutators

Tohoku Mathematical Journal, 2003

We prove sharp weighted norm inequalities for vector-valued singular integral operators and commutators. We first consider the strong (p, p) case with p > 1 and then the weak-type (1, 1) estimate. Our results do not assume any kind of condition on the weight function and involve iterations of the classical Hardy-Littlewood maximal function.

Commutators of singular integrals revisited

Bulletin of the London Mathematical Society

We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing a new result even in the unweighted setting for the first order commutators.