Generalized Sobolev–Morrey estimates for hypoelliptic operators on homogeneous groups
Yazarlar (1)
Prof. Dr. Vagıf GULIYEV
Baku State University, Azerbaycan
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A Matematicas (Q1) | ||
| Dergi ISSN | 1578-7303 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | Türkçe | Basım Tarihi | 02-2021 |
| Cilt / Sayı / Sayfa | 115 / 2 / – | DOI | 10.1007/s13398-021-01009-3 |
| Makale Linki | http://dx.doi.org/10.1007/s13398-021-01009-3 | ||
| 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 |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 1 |
| SCOPUS | 2 |