In this paper, we introduce a class of mappings that is more general than the class of polynomials as well as the class of convex functions. We prove Lp estimates of Marcinkiewicz integral operators along surfaces generated by mappings belong to this class. Moreover, we establish the Lp boundedness of the corresponding maximal functions. Our results extend as well as improve previously known results on Marcinkiewicz integral operators and maximal functions.
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