Some \(\Phi\)-inequalities on spaces of homogeneous type. (Chinese. English summary) Zbl 0908.42009

Long, Shunchao; Wang, Jian

Nat. Sci. J. Xiangtan Univ. 19, No. 2, 24-32 (1997).

In this paper, the authors study the Hardy-Littlewood maximal function \(Mf\), the sharp maximal function \(f^\#\), and certain maximal commutators on the spaces of homogeneous type defined by Coifman and Weiss. Analoguous to well-known results in the Euclidean space, the authors obtain a theorem about the weighted \(\Phi\)-sharp maximal functions, as well as the weighted \(\Phi\)-boundedness of the maximal commutators. As an application, the authors obtain that certain Calderón-Zygmund operators in the Euclidean space are weighted \(\Phi\)-bounded.

Reviewer: Dashan Fan (Milwaukee)

MSC:

42B25	Maximal functions, Littlewood-Paley theory
42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
43A85	Harmonic analysis on homogeneous spaces

Keywords:

weighted \(\Phi\)-inequality; Hardy-Littlewood maximal function; sharp maximal function; spaces of homogeneous type; Calderón-Zygmund operators