NIKOL'SKII-BESOV AND LIZORKIN-TRIEBEL SPACES CONSTRUCTED ON THE BASE OF THE MULTIDIMENSIONAL FOURIER-BESSEL TRANSFORM
Yazarlar (4)
Prof. Dr. Vagıf GULIYEV
Kirsehir Ahi Evran University, Türkiye
Ankara University, Türkiye
Prof. Dr. Ali AKBULUT
Kırşehir Ahi Evran Üniversitesi, Türkiye
Azerbaijan National Academy of Sciences (ANAS), Azerbaycan
| 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 | 01-2011 |
| Cilt / Sayı / Sayfa | 2 / 3 / 42–66 | DOI | – |
| Özet |
| In this paper we define the Nikol'skii-Besov and Lizorkin-Triebel spaces (B-Nikol'skii-Besov and B-Lizorkin-Triebel spaces) in the context of the Fourier-Bessel harmonic analysis. We establish some basic properties of the B-Nikol'skii-Besov and B-Lizorkin-Triebel spaces such as embedding theorems, the lifting property, and characterizing of the Bessel potentials in terms of the B-Lizorkin-Triebel spaces. We prove the inclusion and the density of the Schwartz space in the B-Nikol'skii-Besov and B-Lizorkin-Triebel spaces and prove an interpolation formula for these spaces by the real method. We also prove the Young inequality for the B-convolution operators in the B-Bessel potential spaces. Finally, we give some applications involving the Laplace-Bessel differential operator. |
| Anahtar Kelimeler |
| B-Nikol'skii-Besov spaces | B-Lizorkin-Triebel spaces | Fourier-Bessel transform | B-Bessel potential spaces |