2021/01/04 by Pavel Mozolyako, Georgios Psaromiligkos, Mozolyako, Pavel +5
Mathematics · #42B100 #42B35 #42B99 #47A100 #47A99 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2101.01094
openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Logarithmic potentials and many other potentials satisfy maximum principle. The dyadic version of logarithmic potential can be easily introduced, it lives on dyadic tree and also satisfies maximum principle. But its analog on bi-tree does not have this property. We prove here that "on average" we can still have something like maximum principle on bi-tree. We use the surrogate maximum principle to prove embedding theorems of Carleson type on bi-disc.