Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications

• Autorzy: José María Martell
• Języki publikacji: EN

Abstrakty

EN

In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do not involve the regularity of the kernel. We apply these results to prove the boundedness of holomorphic functional calculi on Lebesgue spaces with Muckenhoupt weights. In particular, some applications are given to second order elliptic operators with different boundary conditions.

Kategorie tematyczne

• 47G10: Integral operators
• 42B25: Maximal functions, Littlewood-Paley theory
• 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47)
• 47A60: Functional calculus
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 161
• Numer: 2
• Strony: 113-145

Daty

wydano

2004

Twórcy

autor

José María Martell

• Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm161-2-2