From the 1 of 7 linked papers with an AI index.
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Sharp higher order regularity of discrete maximal functions
Sung-Yi Liao, José Madrid, Eyvindur Palsson +1
The paper obtains sharp ℓ^p(Z) bounds for the first and second discrete derivatives of the uncentered Hardy‑Littlewood maximal operator applied to binary functions on the integers,…
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…
The smoothest average and some extremal problems for polynomials
José Gaitán, Carlos Garzón, José Madrid
We study the problem of finding the "smoothest'' local average of a function when we consider its convolution with suitable kernels . The measurement…
Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs
Cristian González-Riquelme, Vjekoslav KovaÄ, José Madrid
We study sharp -variational inequalities for the Hardy-Littlewood maximal operator on complete graphs, answering in the affirmative a question by Feng Liu and Qingying Xue. We a…
On suprema of convolutions on discrete cubes
José Gaitan, José Madrid
We find the optimal constant such that \begin{equation*} \|f_1*f_2*\dots*f_{k}\|_{\infty}\geq C\prod_{i=1}^{k}\|f_i\|_1 \end{equation*} for functions $f_i:\{0,1\}^d\to\mathbb{R…