Improved surrogate bi-parameter maximum principle
arXiv:2101.01094
Abstract
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.
15 pages. arXiv admin note: text overlap with arXiv:1906.11145