2009/11/25 by Armen Vagharshakyan, Vagharshakyan, Armen
Mathematics · #42B20 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42B20 #msc:42C40
paper · pdf · doi:10.48550/arxiv.0911.4968
arxiv created 2009/11/25 · arxiv updated 2009/12/08
Any sufficiently smooth one-dimensional Calderon-Zygmund convolution operator is the average of Haar shift operators. The latter are dyadic operators which can be efficiently expressed in terms of the Haar basis. This extends the result of S. Petermichl on restoring Hilbert transform via Haar shift operators, a technique that has become fundamental to the analysis of these operators.