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GENERALIZED WEIGHTED SOBOLEV--MORREY ESTIMATES FOR HYPOELLIPTIC OPERATORS WITH DRIFT ON HOMOGENEOUS GROUPS  
Yazarlar
Prof. Dr. Vagıf GULIYEV Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Özet
Let G = ( RN,◦,δλ ) be a homogeneous group, Q be the homogeneous dimension of G, X0,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 X0 is homogeneous of degree two with respect to the family of dilations ( δλ )λ>0. Consider the following hypoelliptic operator with drift on G (Formula Presented), where (aij) is a constant matrix satisfying the elliptic condition in Rm and a0 ≠ 0. In this paper, for this class of operators we obtain generalized weighted 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 weighted Morrey spaces and proving interpolation results in generalized weighted Sobolev-Morrey spaces on G
Anahtar Kelimeler
Fractional integral operator | Generalized weighted morrey spaces | Generalized weighted sobolev-morrey estimates | Homogeneous groups | Hypoelliptic operators with drift | Singular integral operators
Makale Türü Özgün Makale
Makale Alt Türü SCOPUS dergilerinde yayımlanan tam makale
Dergi Adı Journal of Mathematical Inequalities
Dergi ISSN 1846-579X
Makale Dili İngilizce
Basım Tarihi 01-2022
Cilt No 16
Sayı 1
Sayfalar 219 / 245
Doi Numarası 10.7153/jmi-2022-16-17