### An application of interpolation theory to Fourier series

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We present a method of integration along the lines of the Henstock-Kurzweil integral. All ${L}^{r}$-derivatives are integrable in this method.

The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. Special cases of one of our results give alternative proofs of the...

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