# Singular integral operators with non-smooth kernels on irregular domains.

Xuan Thinh Duong; Alan McIntosh

Revista Matemática Iberoamericana (1999)

- Volume: 15, Issue: 2, page 233-263
- ISSN: 0213-2230

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topDuong, Xuan Thinh, and McIntosh, Alan. "Singular integral operators with non-smooth kernels on irregular domains.." Revista Matemática Iberoamericana 15.2 (1999): 233-263. <http://eudml.org/doc/39575>.

@article{Duong1999,

abstract = {Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type (1,1), hence bounded on Lp(Ω) for 1 < p ≤ 2.iii) We establish sufficient conditions for the maximal truncated operator T* which is defined by T*u(x) = supε>0 |Tεu(x)|, to be Lp bounded, 1 < p < ∞. Applications include weak (1,1) estimates of certain Riesz transforms, and Lp boundedness of holomorphic functional calculi of linear elliptic operators on irregular domains.},

author = {Duong, Xuan Thinh, McIntosh, Alan},

journal = {Revista Matemática Iberoamericana},

keywords = {Espacio de medida; Espacios LP; Operadores lineales; Operadores integrales; Operadores de tipo débil; singular integrals; bounded operators; Hörmander condition; maximal functions; Riesz transforms},

language = {eng},

number = {2},

pages = {233-263},

title = {Singular integral operators with non-smooth kernels on irregular domains.},

url = {http://eudml.org/doc/39575},

volume = {15},

year = {1999},

}

TY - JOUR

AU - Duong, Xuan Thinh

AU - McIntosh, Alan

TI - Singular integral operators with non-smooth kernels on irregular domains.

JO - Revista Matemática Iberoamericana

PY - 1999

VL - 15

IS - 2

SP - 233

EP - 263

AB - Let χ be a space of homogeneous type. The aims of this paper are as follows.i) Assuming that T is a bounded linear operator on L2(χ), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(χ) for 1 < p ≤ 2; our condition is weaker then the usual Hörmander integral condition.ii) Assuming that T is a bounded linear operator on L2(Ω) where Ω is a measurable subset of χ, we give a sufficient condition on the kernel of T so that T is of weak type (1,1), hence bounded on Lp(Ω) for 1 < p ≤ 2.iii) We establish sufficient conditions for the maximal truncated operator T* which is defined by T*u(x) = supε>0 |Tεu(x)|, to be Lp bounded, 1 < p < ∞. Applications include weak (1,1) estimates of certain Riesz transforms, and Lp boundedness of holomorphic functional calculi of linear elliptic operators on irregular domains.

LA - eng

KW - Espacio de medida; Espacios LP; Operadores lineales; Operadores integrales; Operadores de tipo débil; singular integrals; bounded operators; Hörmander condition; maximal functions; Riesz transforms

UR - http://eudml.org/doc/39575

ER -

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