Recovering singular integrals from Haar shifts

Vagharshakyan, Armen

doi:10.1090/S0002-9939-2010-10426-4

Recovering singular integrals from Haar shifts
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by Armen Vagharshakyan PDF

Proc. Amer. Math. Soc. 138 (2010), 4303-4309 Request permission

Abstract:

We recover one-dimensional Calderón-Zygmund convolution operators with sufficiently smooth kernels by means of a properly chosen averaging of certain dyadic shift operators. As a corollary, a sharp $A_2$ inequality for these Calderón-Zygmund operators is derived from a corresponding inequality for dyadic shift operators.

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