Al-Salman, Ahmad; Al-Qassem, Hussain On the \(L^p\) boundedness of rough parametric Marcinkiewicz functions. (English) Zbl 1138.42007 JIPAM, J. Inequal. Pure Appl. Math. 8, No. 4, Paper No. 108, 8 p. (2007). Summary: In this paper, we study the \(L^p\) boundedness of a class of parametric Marcinkiewicz integral operators with rough kernels in \( L(\log^{+}L)(\mathbb{S}^{n-1})\). Our result in this paper solves an open problem left by the authors of [J. Aust. Math. Soc. 72, No. 1, 13–21 (2002; Zbl 0993.42008)]. Cited in 3 Documents MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B15 Multipliers for harmonic analysis in several variables 42B25 Maximal functions, Littlewood-Paley theory Keywords:rough kernels; Fourier transforms; parametric maximal functions Citations:Zbl 0993.42008 PDFBibTeX XMLCite \textit{A. Al-Salman} and \textit{H. Al-Qassem}, JIPAM, J. Inequal. Pure Appl. Math. 8, No. 4, Paper No. 108, 8 p. (2007; Zbl 1138.42007) Full Text: EuDML EMIS