Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A NOTE ON END PROPERTIES OF MARCINKIEWICZ INTEGRAL

  • DING, YONG (Department of Mathematics and Computer Science Nanchang Institute of Aeronautical Technology)
  • Published : 2005.09.01
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Abstract

In this note we give the mapping properties of the Marcinkiewicz integral !-to. at some end spaces. More precisely, we first prove that !-to. is a bounded operator from H$^{1,($\mathbb{R) to H$^{1, ($\mathbb{R). As a corollary of the results above, we obtain again the weak type (1,1) boundedness of $\mu$$_{, but the condition assumed on n is weaker than Stein's condition. Finally, we show that !-to. is bounded from BMO($\mathbb{R) to BMO($\mathbb{R). The results in this note are the extensions of the results obtained by Lee and Rim recently.

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References

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Cited by

  1. Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel vol.66, pp.4, 2014, https://doi.org/10.1007/s11253-014-0957-0
  2. Commutators of Littlewood-Paley operators vol.52, pp.11, 2009, https://doi.org/10.1007/s11425-009-0178-4