On almost everywhere convergence of strong arithmetic means of Fourier series

الأصل · EN

This article establishes a real-variable argument for Zygmund's theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on T, up to passing to a subsequence. Our approach extends to, among other cases, functions that are defined on Tᵈ, which allows us to establish an analogue of Zygmund's theorem in higher dimensions.