A characterization of the complemented translation-invariant subspaces of $H^ 1(\textbf {R})$
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- by Dale E. Alspach PDF
- 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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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 323 (1991), 197-207
- MSC: Primary 43A15; Secondary 46J15
- DOI: https://doi.org/10.1090/S0002-9947-1991-0986683-5
- MathSciNet review: 986683