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Abstract Let f = ( f n ) n ≥ 0 and g = ( g n ) n ≥ 0 be two real-Hilbert-space-valued martingales such that ( g n… Click to show full abstract
Abstract Let f = ( f n ) n ≥ 0 and g = ( g n ) n ≥ 0 be two real-Hilbert-space-valued martingales such that ( g n ) n ≥ 0 is weakly dominated by ( f n ) n ≥ 0 . The paper contains the proof of the inequality ‖ g ‖ W ( Ω ) ≤ 6 ‖ f ‖ L ∞ , where W is the weak- L ∞ space introduced by Bennett, DeVore and Sharpley. As an application, a related estimate for Haar shift operators is established.
Keywords:
weak inequality;
weakly dominated;
haar shift;
shift operators
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2021
Link to full text (if available)
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2021
Link to full text (if available)
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recommendations!