Littlewood-Paley Characterization for Musielak-Orlicz-Hardy Spaces Associated with Operators
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866914443645943808 |
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| author | Shen, Jiawei Chen, Zhitian Long, Shunchao |
| author_facet | Shen, Jiawei Chen, Zhitian Long, Shunchao |
| contents | Let $X$ be a space of homogeneous type. Assume that $L$ is an non-negative second-order self-adjoint operator on $L^2\left(X\right)$ with (heart) kernel associated to the semigroup $e^{ - tL}$ that satisfies the Gaussian upper bound. In this paper, the authors introduce a new characterization of the Musielak-Orlicz-Hardy Space $H_{φ, L}\left(X\right)$ associated with $L$ in terms of the Lusin area function where $φ$ is a growth function. Further, the authors prove that the Musielak-Orlicz-Hardy Space $H_{L,G,φ}\left(X\right)$ associated with $L$ in terms of the Littlewood-Paley function is coincide with $H_{φ, L}\left(X\right)$ and their norms are equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_08393 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Littlewood-Paley Characterization for Musielak-Orlicz-Hardy Spaces Associated with Operators Shen, Jiawei Chen, Zhitian Long, Shunchao Classical Analysis and ODEs Analysis of PDEs 42B20, 42B25, 42B30, 42B35, 46E30, 47B38 Let $X$ be a space of homogeneous type. Assume that $L$ is an non-negative second-order self-adjoint operator on $L^2\left(X\right)$ with (heart) kernel associated to the semigroup $e^{ - tL}$ that satisfies the Gaussian upper bound. In this paper, the authors introduce a new characterization of the Musielak-Orlicz-Hardy Space $H_{φ, L}\left(X\right)$ associated with $L$ in terms of the Lusin area function where $φ$ is a growth function. Further, the authors prove that the Musielak-Orlicz-Hardy Space $H_{L,G,φ}\left(X\right)$ associated with $L$ in terms of the Littlewood-Paley function is coincide with $H_{φ, L}\left(X\right)$ and their norms are equivalent. |
| title | Littlewood-Paley Characterization for Musielak-Orlicz-Hardy Spaces Associated with Operators |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B20, 42B25, 42B30, 42B35, 46E30, 47B38 |
| url | https://arxiv.org/abs/1903.08393 |