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

Revista Matemática Iberoamericana (1990)

- Volume: 6, Issue: 1-2, page 17-41
- ISSN: 0213-2230

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topHan, 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 -

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