A characterization of the complemented translation-invariant subspaces of 𝐻¹(𝑅)

Alspach, Dale E.

doi:10.1090/S0002-9947-1991-0986683-5

A characterization of the complemented translation-invariant subspaces of $H^ 1(\textbf {R})$
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Trans. Amer. Math. Soc. 323 (1991), 197-207 Request permission

Abstract:

The purpose of this paper is to characterize the complemented translation-invariant subspaces of ${H^1}({\mathbf {R}})$ in terms of the zero set of the Fourier transform. It is shown that if $X$ is such a subspace then $X = I(A)$ where $A$ is in the ring generated by arithmetic progressions and lacunary sequences and $A$ is $\varepsilon$-separated for some $\varepsilon > 0$. This proves a conjecture of the author and D. Ullrich.

References

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