16 citations · 65 across the 61 of their papers we have counts for
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Polynomial growth of Bohnenblust--Hille constants on the Hamming cube
Paata Ivanisvili
We prove that the Bohnenblust--Hille constants for Walsh polynomials on the Hamming cube grow at most polynomially in the degree. More precisely, there is an absolute constant …
A counterexample to the Kato conjecture for positive commutators
Rupert L. Frank, Paata Ivanisvili
We disprove the conjectural converse to Kato's positivity criterion for commutators of functions of the canonical position and momentum operators and by showing that the op…
The missing two-point inequality in Weissler's conjecture
Yi C. Huang, Paata Ivanisvili
Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges and . Ivanisvili--Nazarov estab…
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…
The sharp extension norm for a planar sector
Rupert L. Frank, Paata Ivanisvili
We compute explicitly the infimum of the norms of -extension operators for planar sectors and exhibit an extension operator attaining this infimum. This solves an open pro…
Carbery's inequality in the Schatten--von Neumann classes
Ziang Chen, Paata Ivanisvili, Jose Madrid +1
Carbery posed a question of sharpened triangle inequalities for families of operators in the Schatten--von Neumann classes , . He established a weaker form of the des…