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arXiv · 1811.00978

Bi-parameter embedding and measures with restriction energy condition

Nicola Arcozzi·Irina Holmes·Pavel Mozolyako·Alexander Volberg
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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.

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Nicola Arcozzi, Irina Holmes, Pavel Mozolyako, Alexander Volberg. 2018-11-02. Bi-parameter embedding and measures with restriction energy condition. https://arxiv.org/abs/1811.00978

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