Littlewood's Fourier series refers to a specific type of Fourier series developed by mathematician John Littlewood. It focuses on the convergence properties of Fourier series, particularly for functions that may not be smooth or well-behaved. Littlewood's work highlighted how certain series can converge almost everywhere, even if they do not converge uniformly. The significance of Littlewood's Fourier series lies in its implications for harmonic analysis and the study of periodic functions. It provides insights into how Fourier series can represent functions with discontinuities or irregularities, expanding the understanding of Fourier analysis and its applications in various fields, including signal processing and differential equations.