Abstract
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 $L^{p}$ estimates of Marcinkiewicz Mintegral operators along surfaces generated by mappings belong to this class. Moreover, we establish the $L^{p}$ boundedness of the corresponding maximal functions. Our results extend as well as improve previously known results on Marcinkiewicz integral operators and maximal functions.
Citation
Ahmad Al-Salman. "$L^{p}$ bounds for a class of Marcinkiewicz integral operators." J. Integral Equations Applications 31 (2) 165 - 182, 2019. https://doi.org/10.1216/JIE-2019-31-2-165
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