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http://dx.doi.org/10.4134/JKMS.2005.42.5.1087

A NOTE ON END PROPERTIES OF MARCINKIEWICZ INTEGRAL  

DING, YONG (Department of Mathematics and Computer Science Nanchang Institute of Aeronautical Technology)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.5, 2005 , pp. 1087-1100 More about this Journal
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.
Keywords
Marcinkiewicz integral; weak Hardy space; BMO;
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