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We prove strong-type $$A_p$$ A p – $$A_\infty $$ A ∞ estimate for square functions, improving on the $$A_p$$ A p bound due to Lerner. Entropy bounds, in the recent innovation of Treil–Volberg, are then proved. The techniques of proof include parallel stopping cubes, pigeon-hole arguments, and the approach to entropy bounds of Lacey–Spencer.
Mathematische Zeitschrift – Springer Journals
Published: May 20, 2016
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