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