Fractional integral associated to schrödinger operator on the heisenberg groups in vanishing generalized morrey spaces

Küçük Resim Yok

Tarih

2018

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

Künye