most recent 30 from http://mathoverflow.net 2013-05-20T05:12:56Z http://mathoverflow.net/feeds/question/65410 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65410/how-to-prove-this-version-of-schwartz-lemma HKSHLZW 2011-05-19T09:07:04Z 2011-05-19T09:33:19Z

<p>I see this theorem in Hans Grauert &amp; Reinhold Remmert's book 'Theory of stein space' , page 190, in chapter 6 . The classical Schwartz lemma is stated as follows , but i don't know how to prove it. Let $E$ , $E'$ be disks centered at the origin in the $w$-plane with radii <code>$ 0&lt;r'&lt;r $</code>. Let $a:=r'r^{-1}$ . Suppose <code>$h\in {\mathcal{O}}(E)$</code> vanishes of order $e$ at the origin . Then $|h|_{E'}\leq a^{e}|h|_E$ , where $|\cdot|_E$ means the super-norm of functions defined on $E$ .</p>