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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.01095 |
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| _version_ | 1866929695570788352 |
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| author | Bui, The Anh Cowling, Michael G. Duong, Xuan Thinh |
| author_facet | Bui, The Anh Cowling, Michael G. Duong, Xuan Thinh |
| contents | Let $L$ be a positive self-adjoint operator on $L^2(X)$, where $X$ is a $σ$-finite metric measure space. When $α\in (0,1)$, the subordinated semigroup $\{\exp(-tL^α):t \in \mathbb{R}^+\}$ can be defined on $L^2(X)$ and extended to $L^p(X)$. We prove various results about the semigroup $\{\exp(-tL^α):t \in \mathbb{R}^+\}$, under different assumptions on $L$. These include the weak type $(1,1)$ boundedness of the maximal operator $f \mapsto \sup _{t\in \mathbb{R}^+}\exp(-tL^α)f$ and characterisations of Hardy spaces associated to the operator $L$ by the area integral and vertical square function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On subordinated semigroups and Hardy spaces associated to fractional powers of operators Bui, The Anh Cowling, Michael G. Duong, Xuan Thinh Functional Analysis 42B30, 42B35 Let $L$ be a positive self-adjoint operator on $L^2(X)$, where $X$ is a $σ$-finite metric measure space. When $α\in (0,1)$, the subordinated semigroup $\{\exp(-tL^α):t \in \mathbb{R}^+\}$ can be defined on $L^2(X)$ and extended to $L^p(X)$. We prove various results about the semigroup $\{\exp(-tL^α):t \in \mathbb{R}^+\}$, under different assumptions on $L$. These include the weak type $(1,1)$ boundedness of the maximal operator $f \mapsto \sup _{t\in \mathbb{R}^+}\exp(-tL^α)f$ and characterisations of Hardy spaces associated to the operator $L$ by the area integral and vertical square function. |
| title | On subordinated semigroups and Hardy spaces associated to fractional powers of operators |
| topic | Functional Analysis 42B30, 42B35 |
| url | https://arxiv.org/abs/2502.01095 |