- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 A note on generalized parametric Marcinkiewicz integrals Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1099-1115 https://doi.org/10.4134/BKMS.b180053Published online September 30, 2019 Feng Liu Shandong University of Science and Technology Abstract : In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class $\mathcal{F}_\beta({\rm S}^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g_\lambda^{*}$-functions and area integrals are also presented. Keywords : generalized parametric Marcinkiewicz integrals, polynomial compound curves, Grafakos-Stefanov class, homogeneous Triebel-Lizorkin spaces MSC numbers : Primary 42B20, 42B25, 42B99 Downloads: Full-text PDF   Full-text HTML