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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

9 votes
1 answer
1k views

Specifying $L^p$ norms of derivatives

Given a sequence of positive numbers $\{a_n\}$ and $1 < p < \infty$, $p\neq 2$, is it possible to build a function $f\in C^\infty(\mathbb R)$ so that $\|f^{(n)}\|_{L^p(\mathbb R)} = a_n$? For what I …
Andy Raich's user avatar