Maximal subspaces of Besov spaces invariant under multiplication by characters

Johnson, R.

doi:10.1090/S0002-9947-1979-0525680-5

Maximal subspaces of Besov spaces invariant under multiplication by characters
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Trans. Amer. Math. Soc. 249 (1979), 387-407 Request permission

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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