Morrey-type estimates for commutator of fractional integral associated with Schrodinger operators on the Heisenberg group
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
Prof. Dr. Ali AKBULUT Kırşehir Ahi Evran Üniversitesi, Türkiye
Faiq M. Namazov
Baku State University, Azerbaycan
Baku State University, Azerbaycan
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Advances in Difference Equations | ||
| Dergi ISSN | 1687-1839 | ||
| Dergi Tarandığı Indeksler | SCI | ||
| Makale Dili | İngilizce | Basım Tarihi | 08-2018 |
| Cilt / Sayı / Sayfa | 2018 / 1 / – | DOI | 10.1186/s13662-018-1730-8 |
| Makale Linki | https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-018-1730-8 | ||
| Özet |
| Let L = - Delta(Hn) + V be a Schrodinger operator on the Heisenberg group H-n m where the nonnegative potential V belongs to the reverse Holder class RH q , for some q(1) >= Q/2, and Q is the homogeneous dimension of H-n Let b belong to a new Campanato space Lambda(theta)(nu)(rho), and let T-beta(i) be the fractional integral operator associated with L. In this paper, we study the boundedness of the commutators [b,I-beta(L)] with b is an element of Lambda(theta)(nu)(rho) on central generalized Morrey spaces LMp,phi 1(alpha,V)(H-n), generalized Morrey spaces Mp,phi(alpha,V)(H-n), and vanishing generalized Morrey spaces VMp,phi(alpha,V)(H-n) associated with Schrodinger operator, respectively. When b belongs to Lambda(theta)(nu)(rho) with theta > 0, 0 < v < 1 and (phi 1 , phi 2) satisfies some conditions, we show that the commutator operator [b,I-beta(L)] is bounded from LMp,phi 1(alpha,V)to LMp,phi 1 alpha,V(H-n), from Mp,phi 1(alpha,V)(H-n) to Mq,phi 2(alpha,V)(H-n) and from VMp,phi(alpha,V)(1)(H-n) to VMq,phi(alpha,V)(2)(H-n),1/p - 1/q = (beta+ nu)/Q. |
| Anahtar Kelimeler |
| BMO | Campanato space | Central generalized Morrey space | Commutator | Fractional integral | Heisenberg group | Schrödinger operator |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| SCOPUS | 1 |
| Google Scholar | 2 |