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?



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