Related papers: Multilinear local Tb for Square functions

In this short note, we extend a local $Tb$ theorem that was proved in \cite{GHO} to a full multilinear local $Tb$ theorem.

We prove a local Tb Theorem for square functions, in which we assume L^p control of the pseudo-accretive system, with p>1 extending the work of S. Hofmann to domains with Ahlfors-David regular boundaries.

Via the new weight $A_{\vec p}^{\infty}(\varphi)$ and the new $BMO$ function, the authors introduce a new class of multilinear square operators $T$ with generalized kernels. The boundedness of multilinear commutators and multilinear…

A local Tb theorem is an L^2 boundedness criterion by which the question of the global behavior of an operator is reduced to its local behavior, acting on a family of test functions b_Q indexed by the dyadic cubes. We present several…

Let $m\in \mathbb{N}$ and $\vec{b}=(b_{1},\cdots,b_{m})$ be a collection of locally integrable functions. It is proved that $b_{1},b_{2},\cdots, b_{m}\in BMO$ if and only if…

We prove a local $Tb$ theorem under close to minimal (up to certain `buffering') integrability assumptions, conjectured by S. Hofmann (El Escorial, 2008): Every cube is assumed to support two non-degenerate functions $b^1_Q\in L^p$ and…

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.

We prove a multilinear local $T(b)$ theorem that differs from previously considered multilinear local $T(b)$ theorems in using exclusively general testing functions $b$ as opposed to a mix of general testing functions and indicator…

We give a proof of a so-called "local $Tb$" Theorem for singular integrals whose kernels satisfy the standard Calder\'on-Zygmund conditions. The present theorem, which extends an earlier result of M. Christ \cite{Ch}, was proved in…

In this work, we present a bilinear Tb theorem for singular integral operators of Calder\'on-Zygmund type. We prove some new accretive type Littlewood-Paley theory and bilinear paraproduct for a para-accretive function setting. We also…

In this paper, local Tb theorems are studied both in the doubling and non-doubling situation. We prove a local Tb theorem for the class of upper doubling measures. With such general measures, scale invariant testing conditions are required…

A local Tb Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes. We…

We prove a local $Tb$ theorem for paraproducts acting on vector valued functions, with matrix weighted averaging operators. The condition on the weight is that its square is in the $L_2$ associated matrix $A_\infty$ class. We also introduce…

Local Tb theorems with Lp type testing conditions, which are not scale invariant, have been studied widely in the case of the Lebesgue measure. In the non-homogeneous world local Tb theorems have only been proved assuming scale invariant…

We obtain a local two weight $Tb$ theorem with an energy side condition for higher dimensional fractional Calder\'{o}n-Zygmund operators. The proof follows the general outline of the proof for the corresponding one-dimensional $Tb$ theorem…

We give a direct proof of the local $Tb$ Theorem, in the Euclidean setting, and under the assumption of dual exponents. This Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator, supposing the…

Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted…

In this article we extend recent results by the first author on the necessity of $BMO$ for the boundedness of commutators on the classical Lebesgue spaces. We generalize these results to a large class of Banach function spaces. We show that…

We obtain a two weight local Tb theorem for any elliptic and gradient elliptic fractional singular integral operator T on the real line, and any pair of locally finite positive Borel measures on the line. This includes the Hilbert transform…

In this paper, the boundedness properties of commutators generated by $b$ and intrinsic square functions in the endpoint case are discussed, where $b\in BMO(\mathbb R^n)$. We first establish the weighted weak $L\log L$-type estimates for…