THE O'NEIL INEQUALITY FOR THE HANKEL CONVOLUTION OPERATOR AND SOME APPLICATIONS
Yazarlar (3)
C. Aykol Ankara University, Türkiye
Prof. Dr. Vagıf GULIYEV Kirsehir Ahi Evran University, Türkiye
A. Serbetci Ankara University, Türkiye
| Makale Türü | Özgün Makale (ESCI dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | EURASIAN MATHEMATICAL JOURNAL | ||
| Dergi ISSN | 2077-9879 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2013 |
| Cilt / Sayı / Sayfa | 4 / 3 / 8–19 | DOI | – |
| Makale Linki | https://emj.enu.kz/index.php/main/article/view/513 | ||
| Özet |
| In this paper we prove the O’Neil inequality for the Hankel (Fourier-Bessel) convolution operator and consider some of its applications. By using the O’Neil inequality we study the boundedness of the Riesz-Hankel potential operator\(I_ {\beta,\alpha}\), associated with the Hankel transform in the Lorentz-Hankel spaces\(L_ {p, r,\alpha}(0,\infty)\). We establish necessary and sufficient conditions for the boundedness of\(I_ {\beta,\alpha}\) from the Lorentz-Hankel spaces\(L_ {p, r,\alpha}(0,\infty)\) to\(L_ {q, s,\alpha}(0,\infty)\),\(1< p< q<\infty\),\(1\le r\le s\le\infty\). We obtain boundedness conditions in the limiting cases\(p= 1\) and\(p=\frac {2\alpha+ 2}{\beta}\). Finally, for the limiting case\(p=\frac {2\alpha+ 2}{\beta}\) we prove an analogue of the Adams theorem on exponential integrability of\(I_ {\beta,\alpha}\) in\(L_ {\frac {2\alpha+ 2}{\beta}, r,\alpha}(0,\infty)\). |
| Anahtar Kelimeler |
| Bessel differential operator | Hankel transform | alpha-rearrangement | LorentzHankel spaces | Riesz-Hankel potential |
