This paper presents a systematic study for classical aspects of functions with absolutely convergent Fourier series over homogeneous spaces of compact groups. Let be a compact group, be a closed subgroup of , and be the normalized -invariant measure over the left coset space associated with Weil’s formula with respect to the probability measures of and . We introduce the abstract notion of functions with absolutely convergent Fourier series in the Banach function space . We then present some analytic characterizations for the linear space consisting of functions with absolutely convergent Fourier series over the compact homogeneous space .
"Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups." Michigan Math. J. 69 (1) 179 - 200, March 2020. https://doi.org/10.1307/mmj/1574326881