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Mathematics Research Report MRR95-022
Riesz Transforms And Related Singular Integrals
Tadeusz Iwaniec and Gaven Martin
Abstract:
In this paper we study the p-norms of certain singular integral
operators.
A method is
developed for obtaining norm estimates in the case of even kernels
generalising the
classical method of rotation. Along the way we identify the p-norms
of the
scalar Riesz
transformations and other related integral operators. Our methods apply
especially to
the n-dimensional Beurling-Ahlfors transform for which we obtain
new p-norm
estimates.
Other applications are also presented.
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