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A local Hilbert transform, Hardy’s inequality and molecular characterization of Goldberg’s local Hardy space. (English) Zbl 1462.42037

Summary: We prove characterizations of Goldberg’s local Hardy space \(h^1({\mathbb{R}})\) by means of a local Hilbert transform and a molecular decomposition. We use this decomposition to prove a version of Hardy’s inequality for the Fourier transform of functions in this space.

MSC:

42B35 Function spaces arising in harmonic analysis
42B30 \(H^p\)-spaces
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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