77 citations · 243 across the 38 of their papers we have counts for
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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 vecto…
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…
The dyadic Riesz vector II
Komla Domelevo, Stefanie Petermichl
We derive a dyadic model operator for the Riesz vector. We show linear upper bounds for between this model operator and the Riesz vector, when applied to fun…
The dyadic Riesz vector I
Komla Domelevo, Stefanie Petermichl
We derive a dyadic model operator for the Riesz vector. We show linear lower bounds for between this model operator and the Riesz vector, when applied to fun…
The dyadic and the continuous Hilbert transforms with values in Banach spaces. Part2
Komla Domelevo, Stefanie Petermichl
We show that if the dyadic Hilbert transform with values in a Banach space is bounded, then so is the Hilbert transform, with a linear relation of the bounds. This result is…
The dyadic and the continuous Hilbert transforms with values in Banach spaces
Komla Domelevo, Stefanie Petermichl
We show that if the Hilbert transform with values in a Banach space is bounded, then so is the dyadic Hilbert transform, with a linear relation of the norms.