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Full-Text Articles in Physical Sciences and Mathematics
The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh
The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
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.