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- W4310631751 abstract "We investigate the Hardy spaces $H^1_L(X)$ corresponding to self-adjoint operators $L$. Our main aim is to obtain a description of $H^1_L(X)$ in terms of atomic decompositions similar to such characterisation of the classical Hardy spaces $H^1(mathbb{R}^d)$. Under suitable assumptions, such a description was obtained by Yan and the authors in [Trans. Amer. Math. Soc. 375 (2022), no. 9, 6417--6451], where the atoms with respect to an $L$-harmonic function are considered. Here we continue this study and modify the previous definition of atoms. It leads to a more natural and flexible description of Hardy and BMO spaces. We expect that the new definition variant opens the possibility of extending the atomic decomposition of the Hardy spaces $H^1_L(X)$ under less restrictive assumptions." @default.
- W4310631751 created "2022-12-13" @default.
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- W4310631751 date "2022-12-01" @default.
- W4310631751 modified "2023-10-16" @default.
- W4310631751 title "Hardy spaces meet harmonic weights revisited" @default.
- W4310631751 doi "https://doi.org/10.48550/arxiv.2212.00547" @default.
- W4310631751 hasPublicationYear "2022" @default.
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