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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal subspaces of Besov spaces invariant under multiplication by characters


Author: R. Johnson
Journal: Trans. Amer. Math. Soc. 249 (1979), 387-407
MSC: Primary 46E35
MathSciNet review: 525680
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Abstract: Unlike the familiar $ {L^p}$ spaces, neither the homogeneous Besov spaces nor the $ {H^p}$ spaces, $ 0\, < \,p\, < \,\,1$, are closed under multiplication by the functions $ x\, \to \,{e^{i\left\langle {x,h} \right\rangle }}$. We determine the maximal subspace of these spaces which are closed under multiplication by these functions, which are the characters of $ {R^n}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0525680-5
PII: S 0002-9947(1979)0525680-5
Article copyright: © Copyright 1979 American Mathematical Society