 95282 Simon B.
 $L^p$ Norms of the Borel Transform and the Decomposition of Measures
(19K, AMSTeX)
Jun 15, 95

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

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, $F(z)=\int
(xz)^{1}\,d\mu(x)$.
 Files:
95282.tex