2020/11/05 by Cristian González-Riquelme, José Madrid, González-Riquelme, Cristian +1
Mathematics · #05C12 #26A45 #39A12 #43B25 #46E35 #46E39 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2011.02630
openalex publication_date 2020/11/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Let MG be the centered Hardy-Littlewood maximal operator on a finite graph G. We find \undersetp→ ∞lim‖MG‖pp when G is the start graph (Sn) and the complete graph (Kn), and we fully describe ‖MSn‖p and the corresponding extremizers for p∈ (1,2). We prove that \undersetp→ ∞lim‖MSn‖pp =(1+√(n))/(2) when n≥ 25. Also, we compute the best constant \bf CSn,2 such that for every f:V→ ℝ we have Var2MSnf≤ \bf CSn,2 Var2f. We prove that \bf CSn,2=\frac(n2-n-1)1/2n for all n≥ 3 and characterize the extremizers. Moreover, when M is the Hardy-Littlewood maximal operator on ℤ, we compute the best constant \bf Cp such that VarpMf≤ \bf Cp‖f‖p for p∈ ((1)/(2),1) and we describe the extremizers.