The O’Neil inequality for the Hankel convolution operator and some applications
Yazarlar (3)
Canay Aykol Yüce Ankara Üniversitesi, Türkiye
Ayhan Şerbetçi Ankara Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (Uluslararası alan indekslerindeki dergilerde yayınlanan tam makale) | ||
| Dergi Adı | EURASIAN MATHEMATICAL JOURNAL | ||
| Dergi ISSN | 2077-9879 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | MathSciNet | ||
| Makale Dili | İngilizce | Basım Tarihi | 09-2013 |
| 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\(I_ {\beta,\alpha}\), 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\(L_ {\frac {2\alpha+ 2}{\beta}, r,\alpha}(0,\infty)\). |
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