Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents. (19th January 2022)

• Record Type: Journal Article
• Authors: Li, Libo; Hao, Zhiwei
• Other Names: An Tianqing Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-01-19
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/9021391
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.