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Let $ f : U \to \Bbb C$ be a holomorphic function in a neighborhood of 0 (or a polynomial). Is it true that for any integer $ k \geq 1$ , $ $ |f^{(k)}(0)| \leq \|D^k_0 |f|\| \left( = \max_{|u_1|=\dotsb = |u_k|=1} \| D^k_0 |f| (u_1,\dotsc,u_k)\| \right)? $ $ where $ D^k_0 |f|$ isRead more