Carleson measure and balayage
Sandra Pott, Alexander Volberg
TL;DR
This paper investigates the relationship between Carleson measures and their balayages, demonstrating that while balayages are in BMO, the converse does not hold, and provides estimates relating Carleson norms to balayages.
Contribution
It establishes that the balayage of a Carleson measure is not necessarily in the class of measures with Carleson norm estimates, and offers two-sided bounds for these norms.
Findings
Balayages of Carleson measures are in BMO.
The converse statement about balayages is false.
Provides two-sided estimates of Carleson norms in terms of balayages.
Abstract
The balayage of a Carleson measure lies of course in BMO. We show that the converse statement is false. We also make a two-sided estimate of the Carleson norm of a positive measure in terms of balayages.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Banach Space Theory · Advanced Mathematical Physics Problems