TL;DR
This paper explores the relationship between Carleson sequences and balayage to simplify the proof of the equivalence of L1-norms of maximal and square functions in non-homogeneous martingale spaces.
Contribution
It provides a new, simplified proof of a fundamental equivalence in martingale theory using the relation between Carleson sequences and balayage.
Findings
Established the equivalence of L1-norms of maximal and square functions in non-homogeneous martingale settings.
Presented a simplified proof leveraging the relation between Carleson sequences and balayage.
Enhanced understanding of martingale Hardy spaces and their norm equivalences.
Abstract
We investigate the relation between Carleson sequence and balayage, and use this to give an easy proof of the equivalence of the L1-norms of the maximal function and the square function in non-honogeneous martingale settings.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Advanced Banach Space Theory