Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
FORUM MATHEMATICUM(2022)
Abstract
In this paper, the authors introduce weak martingale Hardy-type spaces associated with a quasi-Banach function lattice. The authors then establish the atomic characterizations of these weak martingale Hardy-type spaces. As applications, the authors give the sufficient conditions for the boundedness of sigma-sublinear operators from weak martingale Hardy-type spaces to a quasi-Banach function lattice. Furthermore, the authors clarify the relation among different weak martingale Hardy-type spaces in the framework of a rearrangement-invariant quasi-Banach function space. Finally, the authors apply these results to the weighted Lorentz space and the generalized grand Lebesgue space.
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Key words
Quasi-Banach function lattice, weak martingale Hardy-type spaces, atomic characterization, martingale inequality, rearrangement-invariant
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