The boundedness of the generalized anisotropic potentials with rough kernels in the Lorentz spaces
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Ayhan Serbetci
Ankara Üniversitesi, Türkiye
Ismail Ekincioglu
Dumlupinar Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Integral Transforms and Special Functions (Q3) | ||
| Dergi ISSN | 1065-2469 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2011 |
| Cilt / Sayı / Sayfa | 22 / 12 / 919–935 | DOI | 10.1080/10652469.2010.548334 |
| Özet |
| In this paper, we study the generalized anisotropic potential integral K(alpha,gamma) circle times f and anisotropic fractional integral I(Omega,alpha,gamma) f with rough kernels, associated with the Laplace-Bessel differential operator Delta(B). We prove that the operator f -> K(alpha,gamma) circle times f is bounded from the Lorentz spaces L(p,r,gamma) (R(k)(n),(+)) to L(q,s,gamma) (R(k)(n),(+)) for 1 <= p < q <= infinity, 1 <= r <= s <= infinity. As a result of this, we get the necessary and sufficient conditions for the boundedness of I(Omega,alpha,gamma) from the Lorentz spaces L(p,s,gamma) (R(k)(n),(+)) to L(q,r,gamma) (R(k)(n),(+)), 1 < p < q < infinity, 1 <= r <= s <= 8 and from L(1,r,gamma) (R(k)(n),(+)) to L(q,infinity,gamma) (R(k)(n),(+)) = WL(q,gamma) (R(k)(n),(+)), 1 < q < infinity, 1 <= r <= 8. Furthermore, for the limiting case p = Q/alpha, we give an analogue of Adams' theorem on the exponential integrability of I(Omega,alpha,gamma) in L(Q/alpha,gamma) (R(k)(n),(+)). |
| Anahtar Kelimeler |
| Generalized anisotropic potential integral | Laplace-bessel differential operator | Lorentz spaces | Rough anisotropic fractional integral |