Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents
Let θ≥0 and p· be a variable exponent, and we introduce a new class of function spaces Lp·,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,...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/9021391 |
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| _version_ | 1849398726914736128 |
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| author | Libo Li Zhiwei Hao |
| author_facet | Libo Li Zhiwei Hao |
| author_sort | Libo Li |
| collection | DOAJ |
| description | Let θ≥0 and p· be a variable exponent, and we introduce a new class of function spaces Lp·,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. |
| format | Article |
| id | doaj-art-a5aed357f00149ccbd9ff6e796b8a662 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a5aed357f00149ccbd9ff6e796b8a6622025-08-20T03:38:31ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/9021391Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable ExponentsLibo Li0Zhiwei Hao1College of Mathematics and Computing ScienceCollege of Mathematics and Computing ScienceLet θ≥0 and p· be a variable exponent, and we introduce a new class of function spaces Lp·,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.http://dx.doi.org/10.1155/2022/9021391 |
| spellingShingle | Libo Li Zhiwei Hao Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents Journal of Function Spaces |
| title | Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents |
| title_full | Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents |
| title_fullStr | Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents |
| title_full_unstemmed | Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents |
| title_short | Atomic Decompositions and John-Nirenberg Theorem of Grand Martingale Hardy Spaces with Variable Exponents |
| title_sort | atomic decompositions and john nirenberg theorem of grand martingale hardy spaces with variable exponents |
| url | http://dx.doi.org/10.1155/2022/9021391 |
| work_keys_str_mv | AT liboli atomicdecompositionsandjohnnirenbergtheoremofgrandmartingalehardyspaceswithvariableexponents AT zhiweihao atomicdecompositionsandjohnnirenbergtheoremofgrandmartingalehardyspaceswithvariableexponents |