The Sobolev inequality on the torus revisited

Arpad Benyi, Tadahiro Oh

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 dierences between the periodic setting and
the classical d-dimensional Euclidean one.
Original languageEnglish
Pages (from-to)359-374
Number of pages16
JournalPublicationes Mathematicae Debrecen
Volume83
Issue number3
Publication statusPublished - 2013

Keywords / Materials (for Non-textual outputs)

  • Sobolev spaces
  • Sobolev inequality
  • Fourier series
  • Bessel potential
  • Riesz potential
  • maximal function

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