Abstract
Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on Lp-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions.
| Original language | English |
|---|---|
| Pages (from-to) | 328-338 |
| Number of pages | 11 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 372 |
| Issue number | 1 |
| DOIs | |
| State | Published - Dec 2010 |
Bibliographical note
Funding Information:✩ The research was partially supported by the RFFI 08-01-00302, NSH-3252.2010.1, MTM 2008-05561-C02-02, and 2009 SGR 1303.
Funding
✩ The research was partially supported by the RFFI 08-01-00302, NSH-3252.2010.1, MTM 2008-05561-C02-02, and 2009 SGR 1303.
| Funders | Funder number |
|---|---|
| Russian Foundation for Fundamental Investigations | 2009 SGR 1303, MTM 2008-05561-C02-02, 08-01-00302, NSH-3252.2010.1 |
Keywords
- Fourier integrals
- General monotone functions
- Uniform convergence
- Weighted norm inequalities