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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.

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Derivatives of radial functions can be bounded by derivatives in terms of radial distance?

There are many estimates of Sobolev type of the form $$ ||D^{\alpha}f||_1 \le ||\Delta f||_2 $$ for different pairs of norms. For your case the r.h.s. will be one-dimensional in r $||(D^2-\frac{n-1}{r …
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Error of Discrete Fourier Transform on Finite Domain (vs. Continuous FT) in terms of Sobolev...

Also note a paper, but it is in Russian: Kurbatov A.V., Kurbatov V.G. Approximation of (integral) FT via DFT. http://www.vestnik.vsu.ru/program/view/view.asp?sec=physmath&year=2012&num=02&f_name=2012 …
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