| Yazarlar |
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye |
| Özet |
| Let G= (RN, ∘ , δλ) be a homogeneous group, Q is the homogeneous dimension of G, X, X1, ... , Xm be left invariant real vector fields on G and satisfy Hörmander's rank condition on RN. Assume that X1, ... , Xm(m≤ N- 1) are homogeneous of degree one and X is homogeneous of degree two with respect to the family of dilations (δλ) λ>. Consider the following hypoelliptic operator with drift on GL=∑i,j=1maijXiXj+a0X0,where (aij) is a m× m constant matrix satisfying the elliptic condition in Rm and a≠ 0. In this paper, for this class of operators, we obtain the generalized Sobolev--Morrey estimates by establishing boundedness of a large class of sublinear operators Tα, α∈ [0 , Q) generated by Calderón--Zygmund operators (α= 0) and generated by fractional integral operator (α> 0) on generalized Morrey spaces and proving interpolation results on generalized Sobolev--Morrey spaces on G. The sublinear operators under consideration contain integral operators of harmonic analysis such as Hardy--Littlewood and fractional maximal operators, Calderón--Zygmund operators, fractional integral operators on homogeneous groups, etc. |
| Anahtar Kelimeler |
| Fractional integral operator | Generalized Morrey space | Generalized Sobolev--Morrey estimates | Homogeneous group | Hypoelliptic operators with drift | Singular integral operators |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SCOPUS dergilerinde yayımlanan tam makale |
| Dergi Adı | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |
| Dergi ISSN | 1578-7303 |
| Makale Dili | İngilizce |
| Basım Tarihi | 04-2021 |
| Cilt No | 115 |
| Sayı | 2 |
| Doi Numarası | 10.1007/s13398-021-01009-3 |
