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 dimension-free discrete Remez-type inequality on the polytorus
Joseph Slote, Alexander Volberg, Haonan Zhang
Consider a function from the -fold product of multiplicative cyclic groups of order . Any such may be extended via its Fourier expansion to an a…
Dimension-free discretizations of the uniform norm by small product sets
Lars Becker, Ohad Klein, Joseph Slote +2
Let be an analytic polynomial of degree at most . A classical inequality of Bernstein compares the supremum norm of over the unit circle to its supremum norm over the…