95-282 Simon B.

$L^p$ Norms of the Borel Transform and the Decomposition of Measures (19K, AMSTeX) Jun 15, 95

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Abstract. We relate the decomposition over $[a,b]$ of a measure $d\mu$ (on $\Bbb R$) into absolutely continuous, pure point, and singular continuous pieces to the behavior of integrals $\int\limits ^{b}_{a}(\text{Im}\,F(x+i\epsilon))^{p}\,dx$ as $\epsilon\downarrow 0$. Here $F$ is the Borel transform of $d\mu$, that is, $F(z)=\int (x-z)^{-1}\,d\mu(x)$.

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