Cotlar's identity extends to martingale transforms, revealing that the vector of Riesz transforms in odd dimensions has the same L^p structure as the Hilbert transform, with matching asymptotic norms as p tends to infinity.
Janakiraman,Best weak-type(p, p)constants,1≤p≤2, for orthogonal harmonic functions and martingales, Illinois Journal of Mathematics48(2004), no
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Cotlar martingale transforms and related singular integrals
Cotlar's identity extends to martingale transforms, revealing that the vector of Riesz transforms in odd dimensions has the same L^p structure as the Hilbert transform, with matching asymptotic norms as p tends to infinity.