Abstract
Weighted (L p , L q ) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón-type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the conditions on weights is discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 1949-2003 |
| Number of pages | 55 |
| Journal | Indiana University Mathematics Journal |
| Volume | 67 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:© Indiana University Mathematics Journal.
Funding
Acknowledgements. The first author was supported by the Russian Science Foundation (grant no. 18-11-00199). The third author was partially supported by the Ministerio de Educación y Ciencia of Spain (grant nos. MTM 2017-87409-P, 2017 SGR 358), by the Alexander von Humboldt Foundation, and by the CERCA Programme of the Generalitat de Catalunya.
| Funders | Funder number |
|---|---|
| Ministerio de Educación y Ciencia of Spain | 2017 SGR 358 |
| Alexander von Humboldt-Stiftung | |
| Generalitat de Catalunya | |
| Russian Science Foundation | 18-11-00199 |
Keywords
- Calderón’s inequalities
- Fourier
- Hankel
- Jacobi
- Mehler-Fock transforms
- Pitt’s inequality