3 citations · 3 across the 4 of their papers we have counts for
5 papers · 1 filter
Differences between the potential theories on a tree and on a bi-tree
Pavel Mozolyako, Alexander Volberg
In this note we give several counterexamples. One shows that small energy majorization on bi-tree fails. The second counterexample shows that partial energy estimate always valid o…
Improved surrogate bi-parameter maximum principle
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg +1
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 s…
Carleson embedding on tri-tree and on tri-disc
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg +1
We prove multi-parameter dyadic embedding theorem for Hardy operator on the multi-tree. We also show that for a large class of Dirichlet spaces in bi-disc and tri-disc this proves…
Counterexamples for bi-parameter Carleson embedding
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg
We build here several counterexamples for two weight bi-parameter Carleson embedding theorem.
Bi-parameter Carleson embeddings with product weights
Nicola Arcozzi, Pavel Mozolyako, Georgios Psaromiligkos +2
Coifman--Meyer multipliers represent a very important class of bi-linear singular operators, which were extensively studied and generalized. They have a natural multi-parameter cou…