A new Carleson measure adapted to multi-level ellipsoid covers

Ankang Yu; Yajuan Yang; Baode Li

doi:10.3934/cpaa.2021115

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2021, Volume 20, Issue 10: 3481-3497. Doi: 10.3934/cpaa.2021115 open access

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A new Carleson measure adapted to multi-level ellipsoid covers

College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

^* Corresponding author
^* Corresponding author

Received: November 30, 2020

Revised: April 30, 2021

Early access: June 2021

Published: October 2021

The project is supported by the Xinjiang Training of Innovative Personnel Natural Science Foundation of China grant 2020D01C048 and the National Natural Science Foundation of China grant 11861062

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We develop highly anisotropic Carleson measure over multi-level ellipsoid covers $ \Theta $ of $ \mathbb{R}^n $ that are highly anisotropic in the sense that the ellipsoids can change rapidly from level to level and from point to point. Then we show that the Carleson measure $ \mu $ is sufficient for which the integral defines a bounded operator from $ H^p(\Theta) $ to $ L^p(\mathbb{R}^{n+1}, \, \mu),\ 0

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Mathematics Subject Classification: Primary: 42B35, 42B30, 30H35; Secondary: 52A30.

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