THE O'NEIL INEQUALITY FOR THE HANKEL CONVOLUTION OPERATOR AND SOME APPLICATIONS
Yazarlar (3)
Ankara University, Türkiye
Prof. Dr. Vagıf GULIYEV
Kirsehir Ahi Evran University, Türkiye
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 | – |
| 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,I-alpha associated with the Hankel transform in the Lorentz-Hankel spaces L-p,(r),(alpha)(0, infinity). We establish necessary and sufficient conditions for the boundedness of I-beta,I-alpha from the Lorentz-Hankel spaces L-p,L-r,L-alpha(0, infinity), 1 < p < q < infinity, 1 <= r <= s < infinity. We obtain boundedness conditions in the limiting cases p = 1 and p = (2 alpha + 2)/beta. Finally, for the limiting case p = (2 alpha + 2)/beta we prove an analogue of the Adams theorem on exponential integrability of I-beta,I-alpha in L(2 alpha+2)/beta,r,alpha(0, infinity). |
| Anahtar Kelimeler |
| Bessel differential operator | Hankel transform | alpha-rearrangement | LorentzHankel spaces | Riesz-Hankel potential |
