Abstract
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.
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 language | English |
|---|---|
| Pages (from-to) | 359-374 |
| Number of pages | 16 |
| Journal | Publicationes Mathematicae Debrecen |
| Volume | 83 |
| Issue number | 3 |
| Publication status | Published - 2013 |
Keywords / Materials (for Non-textual outputs)
- Sobolev spaces
- Sobolev inequality
- Fourier series
- Bessel potential
- Riesz potential
- maximal function