Embedding $L^{1}$ in $L^{1}/H^{1}$
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- by J. Bourgain
- Trans. Amer. Math. Soc. 278 (1983), 689-702
- DOI: https://doi.org/10.1090/S0002-9947-1983-0701518-9
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Abstract:
It is proved that ${L^1}$ is isomorphic to a subspace of ${L^1}/{H^1}$. More precisely, there exists a diffuse $\sigma$-algebra $\mathfrak {S}$ on the circle such that the corresponding expectation ${\mathbf {E}}:{H^\infty } \to {L^\infty }({\mathbf {C}})$ is onto. The method consists in studying certain martingales on the product ${\prod ^{\mathbf {N}}}$.References
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Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 278 (1983), 689-702
- MSC: Primary 46E30; Secondary 42A99, 46B25, 60G46
- DOI: https://doi.org/10.1090/S0002-9947-1983-0701518-9
- MathSciNet review: 701518