Atomic decomposition of predictable martingale Hardy space with variable exponents

Hao, Zhiwei

doi:10.1007/s10587-015-0226-x

Cited by 7 publications

(3 citation statements)

References 23 publications

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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%

“…Since then, the study of martingale Hardy spaces associated with various functional spaces has attracted a steadily increasing interest. For instance, martingale Orlicz-type Hardy spaces were investigated in [3][4][5][6], martingale Lorentz Hardy spaces were studied in [7][8][9], and variable martingale Hardy spaces were developed in [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Martingale Grand Hardy Spaces Via Variable Exponentsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…In martingale theory, Chao and Ombe [26] introduced the fractional integrals for dyadic martingales. The fractional integrals in this section are defined for more general martingale setting as in [13,14] (see also [15,[27][28][29][30][31][32]).…”

Section: The Fractional Integral Operatormentioning

confidence: 99%