7 papers · 1 filter
The Winding Number at the Critical Hölder Exponent 1/3: Failure of Universal Fourier Summation
Rupert L. Frank, Paata Ivanisvili
The degree (or winding number) of a sufficiently regular map is given in terms of its Fourier coefficients by $$ \operatorname{deg} f = \sum_{n\in\…
A Beckmann boundary form of Talagrand's conjecture on the discrete cube
Paata Ivanisvili, Xinyuan Xie, Haonan Zhang
We introduce the Beckmann boundary of a Boolean function \[ \mathsf{B}(f)=\inf_{\operatorname{div} V=Lf}\mathbb E\|V(x)\|_2. \] Here \[ L=\sum_iD_i,\qquad D_i f(x)=\frac{f(x)-f(x^{…
Almost-Orthogonality in Lp Spaces: A Case Study with Grok
Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili +2
Carbery proposed the following sharpened form of triangle inequality for many functions: for any and any finite sequence we have \[ \Big\|\sum_j f_j\B…
Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets
Natanael Alpay, Paata Ivanisvili
We study lower bounds for dyadic square functions of indicator functions. In the case of the dyadic square function we obtain a sharp lower bound: for every measurable $A \…
Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos +1
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent . This follows up on previous work, where such bounds were established for …
Optimal Young's convolutions inequality and its reverse form on the hypercube
David Beltran, Paata Ivanisvili, José Madrid +1
We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube in the diagonal case . As applications, we derive bounds for a…