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I cited a result which characterizes Sobolev spaces of functions of one variable as

$$H^p(a,b):=\{x\in C^{p-1}[a,b]:x^{(p-1)}(t)=α+\int^t_aΨ\,\mathrm ds,\ α\in\mathbb R,\ Ψ\in L^2\},$$where $p\in\mathbb N$,

from page 14 of

A. Kirsch: An Introduction to the Mathematical Theory of Inverse Problems. Springer, New York, 1996.

However, the result in this monograph lacks details for proof. Could any researcher help with references with details?

Thanks!

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