Estimates for maximal singular integrals
Tom 96 / 2003
Colloquium Mathematicum 96 (2003), 167-177
MSC: Primary 42B20, 42B25; Secondary 46B70, 47G30.
DOI: 10.4064/cm96-2-2
Streszczenie
It is shown that maximal truncations of nonconvolution $L^2$-bounded singular integral operators with kernels satisfying Hörmander's condition are weak type $(1,1)$ and $L^p$-bounded for $1< p< \infty $. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar's inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.
