Fractional integral associated to schrödinger operator on the heisenberg groups in vanishing generalized morrey spaces
Küçük Resim Yok
Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let L = -?Hn + V be a Schrödinger operator on the Heisenberg groups Hn, where the nonnegative potential V belongs to the reverse Hölder class RHQ/2 and Q is the homogeneous dimension of Hn. Let b belong to a newBMO?(Hn, ?) space, and let IL ß be the fractional integral operator associated with L. In this paper, we study the boundedness of the operator IL ß and its commutators [b, IL ß ] with b ? BMO?(Hn, ?) on vanishing generalized Morrey spaces VM?,V p,? (Hn) associated with Schrödinger operator. We find the sufficient conditions on the pair (?1, ?2) which ensures the boundedness of the operator IL ß from VM?,V p,?1 (Hn) to LM?,V q,?2 (Hn), 1/p - 1/q = ß/Q. When b belongs to BMO?(Hn, ?) and (?1, ?2) satisfies some conditions, we also show that the commutator operator [b, IL ß ] are bounded from VM?,V p,?1 (Hn) to VM?,V q,?2 (Hn), 1/p - 1/q = ß/Q. © 2018, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.
Açıklama
Anahtar Kelimeler
Bmo, Commutator, Fractional integral, Heisenberg group, Schrödinger operator, Vanishing generalized morrey space
Kaynak
Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
38
Sayı
4
