This paper deals with the Fourier coefficients of a function of class L^p. We give a necessary and sufficient condition for function to be of class L^p for p greater than one.
Sokół, J., & Bansal, D. (2012). Coefficients Bounds in Some Subclass of Analytic Functions. Tamkang Journal of Mathematics, 43(4), 621-630. https://www.airitilibrary.com/Article/Detail?DocID=00492930-201212-201212270034-201212270034-621-630