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Some \(\Phi\)-inequalities on spaces of homogeneous type. (Chinese. English summary) Zbl 0908.42009
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.
42B25 Maximal functions, Littlewood-Paley theory
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
43A85 Harmonic analysis on homogeneous spaces