Sobolev spaces, Sobolev inequality, Fourier series, Bessel potential, Riesz potential, Maximal function
We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical d-dimensional Euclidean one.
Publicationes Mathematicae Debrecen
Required Publisher's Statement
Bényi, Árpád and Oh, Tadahiro, "The Sobolev Inequality on the Torus Revisited" (2013). Mathematics. 44.