A NOTE ON END PROPERTIES OF MARCINKIEWICZ INTEGRAL

Title & Authors
A NOTE ON END PROPERTIES OF MARCINKIEWICZ INTEGRAL
DING, YONG;

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$\small{^{1,}$($\small{\mathbb{R}$) to H$\small{^{1,}$ ($\small{\mathbb{R}$). As a corollary of the results above, we obtain again the weak type (1,1) boundedness of $\small{\mu}$$\small{_{}$, but the condition assumed on n is weaker than Stein's condition. Finally, we show that !-to. is bounded from BMO($\small{\mathbb{R}$) to BMO($\small{\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;
Language
English
Cited by
1.
Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel, Ukrainian Mathematical Journal, 2014, 66, 4, 602
2.
Commutators of Littlewood-Paley operators, Science in China Series A: Mathematics, 2009, 52, 11, 2493
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