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math.FA2026
Dimension-free bounds for Riesz transforms on the Hamming cube via a Bellman function
Komla Domelevo, Paata Ivanisvili, Stefanie Petermichl +1
We give a Bellman-function proof of the dimension-free estimate \[ \Big\| \vec{R} f \Big\|_{L^p(Ω;\,\ell^2)} \lesssim (p-1) \,\|f\|_{L^p(Ω)}, \qquad 2\le p<\infty, \] for the vec…
math.FA2026
A twosided linear estimate and a dyadic reduction of the UMD Conjecture
Komla Domelevo, Stefanie Petermichl
We define a time faithful dyadic shift operator of complexity one, that is an antisymmetric antiinvolution. We show that the Hilbert transform with values in a Banach space is $L^p…