Bi-parameter embedding and measures with restricted energy conditions Academic Article uri icon

abstract

  • Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, and Giulia Sarfatti recently gave the proof of a bi-parameter Carleson embedding theorem. Their proof uses heavily the notion of capacity on bi-tree. In this note we give one more proof of a bi-parameter Carleson embedding theorem that avoids the use of bi-tree capacity. Unlike the proof on a simple tree (in a pervious paper of the authors) that used the Bellman function technique, the proof here is based on some rather subtle comparison of energies of measures on bi-tree.

author list (cited authors)

  • Arcozzi, N., Holmes, I., Mozolyako, P., & Volberg, A.

citation count

  • 2

publication date

  • November 2019