Fractional Integral on Martingale Hardy Spaces With Variable Exponents

Hao, Zhiwei; Jiao, Yong

doi:10.1515/fca-2015-0065

Cited by 36 publications

(19 citation statements)

References 22 publications

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“…Remark 5.12. Recently, there are some new results concerning martingale Hardy spaces with variable exponents; see [11,19,29].…”

Section: The Duality and John-nirenberg Theoremmentioning

confidence: 99%

Martingale Hardy spaces with variable exponents

Jiao¹,

Zhou²,

Hao³

et al. 2016

Banach J. Math. Anal.

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In this paper, we introduce Hardy spaces with variable exponents defined on a probability space and develop the martingale theory of variable Hardy spaces. We prove the weak type and strong type inequalities on Doob's maximal operator and get a $(1,p(\cdot),\infty)$-atomic decomposition for Hardy martingale spaces associated with conditional square functions. As applications, we obtain a dual theorem and the John-Nirenberg inequalities in the frame of variable exponents. The key ingredient is that we find a condition with probabilistic characterization of $p(\cdot)$ to replace the so-called log-H\"{o}lder continuity condition in $\mathbb {R}^n.$Comment: Banach Journal of Mathematical Analysis, to appea

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“…Remark 5.12. Recently, there are some new results concerning martingale Hardy spaces with variable exponents; see [11,19,29].…”

Section: The Duality and John-nirenberg Theoremmentioning

confidence: 99%

Martingale Hardy spaces with variable exponents

Jiao¹,

Zhou²,

Hao³

et al. 2016

Banach J. Math. Anal.

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“…The following lemma was proved in Cruze-Uribe and Fiorenza [1] and Hao and Jiao [3]. Lemma 1 Let pðÁÞ 2 P satisfy (1).…”

Section: \1mentioning

confidence: 97%

Boundedness of dyadic maximal operators on variable Lebesgue spaces

Weisz

2020

Adv. Oper. Theory

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“…Remark 3. If θ = 0, then we obtain the definitions of [10,12,27]). If we consider the special case θ = 1 and pð•Þ ≡ p with the notations above, we obtain the definitions of H * pÞ , H S pÞ , H s pÞ , Q pÞ , and D pÞ , respectively (see [26]).…”

Section: Martingale Grand Hardy Spaces Via Variable Exponentsmentioning

confidence: 99%

“…Compared with Euclidean space ℝ n , the probability space ðΩ, ℙÞ has no natural metric structure. Fortunately, Jiao et al [11,27] put forward the following condition: there exists an absolute constant κ ≥ 1 depending only on pð…”

Section: The Generalized John-nirenberg Theoremmentioning

confidence: 99%

Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents

Hao

2022

Journal of Function Spaces

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Let θ ≥ 0 and p · be a variable exponent, and we introduce a new class of function spaces L p · , θ in a probabilistic setting which unifies and generalizes the variable Lebesgue spaces with θ = 0 and grand Lebesgue spaces with p · ≡ p and θ = 1 . Based on the new spaces, we introduce a kind of Hardy-type spaces, grand martingale Hardy spaces with variable exponents, via the martingale operators. The atomic decompositions and John-Nirenberg theorem shall be discussed in these new Hardy spaces.

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Fractional Integral on Martingale Hardy Spaces With Variable Exponents

Abstract: In this paper we investigate the boundedness of fractional integral operators on predictable martingale Hardy spaces with variable exponents defined on a probability space. More precisely, let f = (f

Cited by 36 publications

References 22 publications

Martingale Hardy spaces with variable exponents

Martingale Hardy spaces with variable exponents

Boundedness of dyadic maximal operators on variable Lebesgue spaces

Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents

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