H1 , BMO, and John–Nirenberg Inequality on LCA Groups

Article Type

Research Article

Publication Title

Mediterranean Journal of Mathematics

Abstract

Let G be a locally compact Abelian (LCA) group which possesses a covering family. We define an atomic Hardy space H1(G) and BMO (G) of functions of bounded mean oscillation. We prove that the dual space of H1(G) is BMO (G) and that John–Nirenberg-type inequality for functions in BMO (G) holds. Finally, we show that our theory is strong enough to give H1(G) - L1(G) estimates for certain convolution operators.

DOI

https://10.1007/s00009-023-02256-x

Publication Date

4-1-2023

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