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

Duong, 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 &lt; 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 &lt; p ≤ 2.iii) We establish sufficient conditions for the maximal truncated operator T* which is defined by T*u(x) = supε&gt;0 |Tεu(x)|, to be Lp bounded, 1 &lt; p &lt; ∞. 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 &lt; 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 &lt; p ≤ 2.iii) We establish sufficient conditions for the maximal truncated operator T* which is defined by T*u(x) = supε&gt;0 |Tεu(x)|, to be Lp bounded, 1 &lt; p &lt; ∞. 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 -