Martingale transforms between Orlicz–Hardy spaces of predictable martingales

Lin, Yong; Dan, Zhuang

doi:10.1016/j.jmaa.2013.12.043

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Cited by 5 publications

(2 citation statements)

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“…We note that the "infimum" taken in P p,q and Q p,q norms is attained [23]. Henceforth, such an "infimum" sequence will be referred to as optimal.…”

Section: Martingalementioning

confidence: 99%

Martingale Transforms between Martingale Hardy-amalgam Spaces

Bansah

2021

Abstract and Applied Analysis

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We discuss martingale transforms between martingale Hardy-amalgam spaces H p , q s , Q p , q and P p , q . Let 0 < p < q < ∞ , p 1 < p and q 1 < q and let f = f n , n ∈ ℕ be a martingale in P p 1 , q 1 ; then, we show that its martingale transforms are the martingales in P p , q for some p , q and similarly for H p , q s and Q p , q .

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“…We note that the "infimum" taken in P p,q and Q p,q norms is attained [23]. Henceforth, such an "infimum" sequence will be referred to as optimal.…”

Section: Martingalementioning

confidence: 99%

Martingale Transforms between Martingale Hardy-amalgam Spaces

Bansah

2021

Abstract and Applied Analysis

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“…It is known that Orlicz spaces L and Orlicz-Hardy spaces H are very useful to know more precise properties of functions and martingales (see for example [1]- [3], [8], [14], [15], [21]- [23]). In martingale theory, martingale Orlicz-Hardy spaces H associated with concave functions , which are the generalizations of Hardy spaces H p for 0 < p ≤ 1, were introduced recently by Miyamoto, Nakai and Sadasue [14] and also were investigated by Jiao and Yu [8].…”

Section: Introductionmentioning

confidence: 99%

Duality theorem for B‐valued martingale Orlicz–Hardy spaces associated with concave functions

Lin

2016

Mathematische Nachrichten

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The dual space of B-valued martingale Orlicz-Hardy space H s( p) (B) with a concave function , which is associated with the conditional p-variation of B-valued martingale, is characterized. To obtain the results, a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.

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Dual spaces of weak Orlicz–Hardy spaces for vector-valued martingales

Lin

2016

Journal of Mathematical Analysis and Applications

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Martingale transforms between Orlicz–Hardy spaces of predictable martingales

Cited by 5 publications

References 11 publications

Martingale Transforms between Martingale Hardy-amalgam Spaces

Martingale Transforms between Martingale Hardy-amalgam Spaces

Duality theorem for B‐valued martingale Orlicz–Hardy spaces associated with concave functions

Dual spaces of weak Orlicz–Hardy spaces for vector-valued martingales

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