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1. CMB 2010 (vol 54 pp. 100)
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On the Generalized Marcinkiewicz Integral Operators with Rough Kernels A class of generalized Marcinkiewicz
integral operators is introduced, and, under rather weak conditions
on the integral kernels, the boundedness of such operators on $L^p$
and Triebel--Lizorkin spaces is established.
Keywords: Marcinkiewicz integral, Littlewood--Paley theory, Triebel--Lizorkin space, rough kernel, product domain Categories:42B20, , , , , 42B25, 42B30, 42B99 |
2. CMB 2000 (vol 43 pp. 63)
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Sharpness Results and Knapp's Homogeneity Argument We prove that the $L^2$ restriction theorem, and $L^p \to L^{p'}$,
$\frac{1}{p}+\frac{1}{p'}=1$, boundedness of the surface averages
imply certain geometric restrictions on the underlying
hypersurface. We deduce that these bounds imply that a certain
number of principal curvatures do not vanish.
Category:42B99 |