Related papers: A local $T(b)$ theorem for perfect multilinear Cal…

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

Local $Tb$ theorems with $L^p$ type testing conditions, which are not scale invariant, have been studied widely in the case of the Lebesgue measure. Until very recently, local $Tb$ theorems in the non-homogeneous case had only been proved…

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…

We demonstrate and develop dyadic-probabilistic methods in connection with non-homogeneous bilinear operators, namely singular integrals and square functions. We develop the full non-homogeneous theory of bilinear singular integrals using a…

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

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…

We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…

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 variant of the global $T(1)$ criterion to characterize the bounded Calder\'{o}n--Zygmund operators on BMO($\mathbb{R}^d$) is proved. We apply it to the certain Calder\'on commutators.

We provide an alternative proof of a (local) T1 theorem for dual exponents in the non-homogeneous setting of upper doubling measures. This previously known theorem provides necessary and sufficient conditions for the L^p-boundedness of…

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 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…

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 develop a new general method to prove various non-doubling local Tb theorems. The method combines the non-homogeneous good lambda method of Tolsa, the big pieces Tb theorem of Nazarov-Treil-Volberg and a new change of measure argument…

In this paper, we prove a version of the typed B\"ohm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a…

We prove a Tb Theorem that characterizes all Calderon-Zygmund operators that extend compactly on L^p(R^n), 1<p<\infty . The result, whose proof does not require the property of accretivity, can be used to prove compactness of the Double…

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…

Perfect dyadic operators were first introduced in \cite{AHMTT}, where a local $T(b)$ theorem was proved for such operators. In \cite{AY} it was shown that for every singular integral operator $T$ with locally bounded kernel on $\mathbb{R}^n…