English

Improved surrogate bi-parameter maximum principle

Analysis of PDEs 2021-01-11 v2 Classical Analysis and ODEs

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.

Cite

@article{arxiv.2101.01094,
  title  = {Improved surrogate bi-parameter maximum principle},
  author = {Pavel Mozolyako and Georgios Psaromiligkos and Alexander Volberg and Pavel Zorin-Kranich},
  journal= {arXiv preprint arXiv:2101.01094},
  year   = {2021}
}

Comments

15 pages. arXiv admin note: text overlap with arXiv:1906.11145

R2 v1 2026-06-23T21:45:48.364Z