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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