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

Título inglés Singular integral operators with non-smooth kernels on irregular domains.
Título español Operadores integrales singulares con núcleo no suave en dominios irregulares.
Autor/es Duong, Xuan Thinh ; McIntosh, Alan
Organización Sch. Math. Phys. Comput. Electron. Macquarie Univ., Port Macquarie, Australia
Revista 0213-2230
Publicación 1999, 15 (2): 233-263, 26 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120217
Palabras clave español Espacio de medida ; Espacios LP ; Operadores lineales ; Operadores integrales ; Operadores de tipo débil
Código MathReviews MR1715407
Código Z-Math Zbl 0980.42007
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