Norm Inequalities for the Fourier Coefficients of Some Almost Periodic Functions

2019/05/16 by Boryshchak, Y., Myers, A., Sagher, Y.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.06899

Abstract

Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to prove norm inequalities for Besicovitch almost periodic functions. This yields an analogue of Paley's Inequality for the Fourier coefficients of periodic functions.

Related

• Order of Magnitude of Fourier Coefficients for Almost Periodic Functions
• Direct and inverse approximation theorems in the Besicovitch-Museilak-Orlicz spaces of almost periodic functions
• Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces
• Sets of values of equivalent almost periodic functions
• Actual problems of the approximation theory in metrics of discrete spaces on sets of summable periodic and almost periodic functions