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