Para-accretive functions, the weak boundedness property and the Tb theorem.

Han, Yongsheng, and Sawyer, Eric T.. "Para-accretive functions, the weak boundedness property and the Tb theorem.." Revista Matemática Iberoamericana 6.1-2 (1990): 17-41. <http://eudml.org/doc/39397>.

@article{Han1990,
abstract = {G. David, J.-L. Journé and S. Semmes have shown that if b1 and b2 are para-accretive functions on Rn, then the Tb theorem holds: A linear operator T with Calderón-Zygmund kernel is bounded on L2 if and only if Tb1 ∈ BMO, T*b2 ∈ BMO and Mb2TMb1 has the weak boundedness property. Conversely they showed that when b1 = b2 = b, para-accretivity of b is necessary for Tb Theorem to hold. In this paper we show that para-accretivity of both b1 and b2 is necessary for the Tb Theorem to hold in general. In addition, we give a characterization of para-accretivity in terms of the weak boundedness property and use this to give a sharp Tb Theorem for Besov and Triebel-Lizorkin spaces.},
author = {Han, Yongsheng, Sawyer, Eric T.},
journal = {Revista Matemática Iberoamericana},
keywords = {Función armónica; Acotación; Acreción; Dimensión débil; singular integral; Besov space; Caldéron-Zygmund; BMO; para- accretivity; Tb theorem; weak boundedness; Triebel-Lizorkin spaces},
language = {eng},
number = {1-2},
pages = {17-41},
title = {Para-accretive functions, the weak boundedness property and the Tb theorem.},
url = {http://eudml.org/doc/39397},
volume = {6},
year = {1990},
}

TY - JOUR
AU - Han, Yongsheng
AU - Sawyer, Eric T.
TI - Para-accretive functions, the weak boundedness property and the Tb theorem.
JO - Revista Matemática Iberoamericana
PY - 1990
VL - 6
IS - 1-2
SP - 17
EP - 41
AB - G. David, J.-L. Journé and S. Semmes have shown that if b1 and b2 are para-accretive functions on Rn, then the Tb theorem holds: A linear operator T with Calderón-Zygmund kernel is bounded on L2 if and only if Tb1 ∈ BMO, T*b2 ∈ BMO and Mb2TMb1 has the weak boundedness property. Conversely they showed that when b1 = b2 = b, para-accretivity of b is necessary for Tb Theorem to hold. In this paper we show that para-accretivity of both b1 and b2 is necessary for the Tb Theorem to hold in general. In addition, we give a characterization of para-accretivity in terms of the weak boundedness property and use this to give a sharp Tb Theorem for Besov and Triebel-Lizorkin spaces.
LA - eng
KW - Función armónica; Acotación; Acreción; Dimensión débil; singular integral; Besov space; Caldéron-Zygmund; BMO; para- accretivity; Tb theorem; weak boundedness; Triebel-Lizorkin spaces
UR - http://eudml.org/doc/39397
ER -