Weighted norm inequalities for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. (English) Zbl 1513.42052
Summary: In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight \(\omega\) considered here belongs to the Muckenhoupt’s class \(A_\infty\). Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42B35 | Function spaces arising in harmonic analysis |
Keywords:
commutators; Muckenhoupt weights; Marcinkiewicz integrals; singular integrals; sharp maximal functions; BMO functions; Young functions; Luxemburg norm; spaces of homogeneous typeReferences:
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