Improved surrogate bi-parameter maximum principle

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.

arXiv comment15 pages. arXiv admin note: text overlap with arXiv:1906.11145

References in corpus (5)

• Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II
• Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, I
• Sparse Domination for Bi-Parameter Operators Using Square Functions
• Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc
• Bi-parameter Carleson embeddings with product weights

Cited by in corpus (1)

• Differences between the potential theories on a tree and on a bi-tree