Weak Orlicz-Hardy Martingale Spaces

TL;DR

This paper introduces weak Orlicz-Hardy martingale spaces linked to concave functions, establishes atomic decompositions, explores operator boundedness, and investigates duality and inequalities, extending existing Orlicz-Hardy space theory.

Contribution

It presents new weak Orlicz-Hardy martingale spaces, proves atomic decomposition theorems, and analyzes duality and boundedness properties, extending prior work on Orlicz-Hardy spaces.

Findings

Established weak atomic decomposition theorems.

Provided a sufficient condition for operator boundedness.

Derived a new John-Nirenberg type inequality.

Abstract

In this paper, several weak Orlicz-Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient condition for a sublinear operator defined on the weak Orlicz-Hardy martingale spaces to be bounded is given. Further, we investigate the duality of weak Orlicz-Hardy martingale spaces and obtain a new John-Nirenberg type inequality when the stochastic basis is regular. These results can be regarded as weak versions of the Orlicz-Hardy martingale spaces due to Miyamoto, Nakai and Sadasue.