Abstract
Let G be a locally compact Abelian (LCA) group which possesses a covering family. We define an atomic Hardy space \(H^1(G)\) and \(\textrm{BMO}(G)\) of functions of bounded mean oscillation. We prove that the dual space of \(H^1(G)\) is \(\textrm{BMO}(G)\) and that John–Nirenberg-type inequality for functions in \(\textrm{BMO}(G)\) holds. Finally, we show that our theory is strong enough to give \(H^1(G)-L^1(G)\) estimates for certain convolution operators.
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Acknowledgements
It is the greatest pleasure to express my gratitude and thanks to Biswaranjan Behera, my advisor, for his careful reading of this paper and for providing many valuable suggestions.
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Molla, M.N. \(H^1\), BMO, and John–Nirenberg Inequality on LCA Groups. Mediterr. J. Math. 20, 55 (2023). https://doi.org/10.1007/s00009-023-02256-x
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DOI: https://doi.org/10.1007/s00009-023-02256-x