On rough maximal operators and Marcinkiewicz integrals along submanifolds

Volume 190 / 2009

H. M. Al-Qassem, Y. Pan Studia Mathematica 190 (2009), 73-98 MSC: Primary 42B20; Secondary 42B15, 42B25. DOI: 10.4064/sm190-1-3


We investigate the $L^{p}$ boundedness for a class of parametric Marcinkiewicz integral operators associated to submanifolds and a class of related maximal operators under the $L(\log L)^{\alpha}({\mathbb S} ^{n-1})$ condition on the kernel functions. Our results improve and extend some known results.


  • H. M. Al-QassemDepartment of Mathematics and Physics
    Qatar University
    Doha, Qatar
  • Y. PanDepartment of Mathematics
    University of Pittsburgh
    Pittsburgh, PA 15260, U.S.A.

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