4 papers
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…
The Poisson Matrix characteristic and the 3/2 blow up of the Hilbert transform
Komla Domelevo, Spyridon Kakaroumpas, Stefanie Petermichl +2
Recently the matrix conjecture was disproved. Indeed, the growth of the vector Hilbert transform in the matrix weighted space was shown to be at best a constant mult…
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…
Dimension-free estimates for low degree functions on the Hamming cube
Komla Domelevo, Polona Durcik, Valentia Fragkiadaki +4
The main result of this paper are dimension-free inequalities, , for low degree scalar-valued functions on the Hamming cube. More precisely, for any $\vare…