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Martingale transforms between Orlicz–Hardy spaces of predictable martingales

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Volume
413
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2013.12.043
Keywords
  • Martingale Transforms
  • Young Functions
  • Orlicz–Hardy Spaces
Disciplines
  • Mathematics

Abstract

Abstract Using the technique of Burkholderʼs martingale transforms, the relations between “predictable” martingale Orlicz–Hardy spaces are investigated. Let Φ1 and Φ2 be two Young functions and Φ1⋞Φ2 in some sense, a constructive proof is obtained of that the elements in Orlicz–Hardy space HΦ1 are none other than the martingale transforms of those in Orlicz–Hardy space HΦ2, where HΦ∈{PΦ,QΦ,HΦs}. At the endpoint case, the space H∞ must be replaced by a BMO space, it is also proved that a martingale is in HΦ∈{PΦ,QΦ} if and only if it is the transform of a martingale from BMO∈{BMO1,BMO2}.

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