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2 results

  • A NOTE ON MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION

  • Part of
  • FENG LIU
  • Journal:
    Journal of the Australian Mathematical Society / Volume 104 / Issue 3 / June 2018
    Published online by Cambridge University Press:
    14 August 2017, pp. 380-402
    Print publication:
    June 2018
    • Article
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  • We establish the bounds of Marcinkiewicz integrals associated to surfaces of revolution generated by two polynomial mappings on Triebel–Lizorkin spaces and Besov spaces when their integral kernels are given by functions $\unicode[STIX]{x1D6FA}\in H^{1}(\text{S}^{n-1})\cup L(\log ^{+}L)^{1/2}(\text{S}^{n-1})$. Our main results represent improvements as well as natural extensions of many previously known results.

  • $L^{p}$ BOUNDS FOR MARCINKIEWICZ INTEGRALS

  • Yong Ding, Yibiao Pan
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 46 / Issue 3 / October 2003
    Published online by Cambridge University Press:
    10 December 2003, pp. 669-677
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  • In this paper the authors establish the $L^p$ boundedness for several classes of Marcinkiewicz integral operators with kernels satisfying a condition introduced by Grafakos and Stefanov in Indiana Univ. Math. J.47 (1998), 455–469.

    AMS 2000 Mathematics subject classification: Primary 42B25; 42B99