This article is cited in 10 papers

Embedding theorems and a characterization of traces in the spaces $H^p(U^n)$, $0<p<\infty$

F. A. Shamoyan


Abstract: A complete characterization is obtained of the measures $d\mu$ on the unit disk $U$ for which the operator $Df(z)=f(z,z,\dots,z)$ maps $H^p(U^n)$ into $L^p(d\mu)$, $0< p<\infty$. The solution to a problem of W. Rudin is obtained as a corollary.
Bibliography: 16 titles.

UDC: 517.555

MSC: 32A35, 46E35

Received: 28.12.1977

 English version: Mathematics of the USSR-Sbornik, 1979, 35:5, 709–725

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