Abstract
For the asymptotic formula for the Fourier sine transform of a function of bounded variation, we find a new proof entirely within the framework of the theory of Hardy spaces, primarily with the use of the Hardy inequality. We show that, for a function of bounded variation whose derivative lies in the Hardy space, every aspect of the behavior of its Fourier transform can somehow be expressed in terms of the Hilbert transform of the derivative.
| Original language | English |
|---|---|
| Pages (from-to) | 93-99 |
| Number of pages | 7 |
| Journal | Mathematical Notes |
| Volume | 100 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 1 Jul 2016 |
Bibliographical note
Publisher Copyright:© 2016, Pleiades Publishing, Ltd.
Keywords
- Fourier transform
- Hardy inequality
- Hardy space
- Hilbert transform
- M. Riesz theorem
- function of bounded variation
- locally absolutely continuous function