Conditions for restricted translation operators to belong to 𝑆_{𝑝}

Dym, Harry; Shapiro, Isidor

doi:10.1090/S0002-9939-1977-0448143-8

Conditions for restricted translation operators to belong to $S_{p}$
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by Harry Dym and Isidor Shapiro PDF

Proc. Amer. Math. Soc. 63 (1977), 251-258 Request permission

Abstract:

Let B be a Blaschke product, let P be the orthogonal projection of ${L^2}({R^1})$ onto the left invariant subspace ${H^2} \ominus B{H^2}$ and let ${E_t}:f(\gamma ) \to {e^{ - i\gamma t}}f(\gamma )$. Conditions are given on the roots of B for $P{E_t}P$ to belong to ${S_p}, 0 < p < \infty$.

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