Abstract
A function f with bounded variation and integrable Hilbert transform of df is locally absolutely continuous. We give a direct real-valued proof of this result and connect it with integrability problems for the Fourier transform of a function with bounded variation, in particular, with a Hardy-Littlewood theorem.
Original language | English |
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Pages (from-to) | 337-341 |
Number of pages | 5 |
Journal | Georgian Mathematical Journal |
Volume | 21 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2014 |
Bibliographical note
Publisher Copyright:© 2014 by De Gruyter 2014.
Keywords
- Absolute continuity
- Fourier transform
- HardyLittlewood theorem
- Hilbert transform
- bounded variation
- measure
- theorem of the brothers Riesz