Marcinkiewicz integrals associated with Schrödinger operator and their commutators on vanishing generalized Morrey spaces
| Yazarlar (3) |
Prof. Dr. Ali AKBULUT
Ahi Evran Üniversitesi, Türkiye |
Prof. Dr. Vagıf GULIYEV
Ahi Evran Üniversitesi, Türkiye |
Mehriban N Omarova
|
| Özet |
| Let L = -Delta + V be a Schrodinger operator, where Delta is the Laplacian on R-n and the non-negative potential V belongs to the reverse Holder class RHq for q >= n/2. In this paper, we study the boundedness of the Marcinkiewicz integral operators mu(L)(j) and their commutators [b, mu(L)(j)] with b is an element of BMO theta (rho) on generalized Morrey spaces M-p,phi(alpha,V) (R-n) associated with Schrodinger operator and vanishing generalized Morrey spaces VMp,phi alpha,V (R-n) associated with Schrodinger operator. We find the sufficient conditions on the pair (phi(1), phi(2)) which ensure the boundedness of the operators mu(L)(j) from one vanishing generalized Morrey space VMp,phi 1 alpha,V to another VMp,phi 2 alpha,V, 1 < p < infinity and from the space VM1,phi 1 alpha,V to the weak space VWM1,phi 2 alpha,V. When b belongs to BMO theta (rho) and (phi(1), phi(2)) satisfies some conditions, we also show that [b, mu(L)(j)] is bounded from M-p,phi 1(alpha,V) to M-p,M-phi 2(alpha,V) and from VMp,phi 1 alpha,V to VMp,phi 2 alpha,V, 1 < p < infinity. |
| Anahtar Kelimeler |
| BMO | commutator | Marcinkiewicz integral | Schrödinger operator | vanishing generalized Morrey space |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale |
| Dergi Adı | BOUNDARY VALUE PROBLEMS |
| Dergi ISSN | 1687-2770 Wos Dergi Scopus Dergi |
| Dergi Tarandığı Indeksler | SCI-Expanded |
| Makale Dili | İngilizce |
| Basım Tarihi | 08-2017 |
| Cilt No | 2017 |
| Sayı | 1 |
| Doi Numarası | 10.1186/s13661-017-0851-4 |
| Makale Linki | http://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-017-0851-4 |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 14 |
| SCOPUS | 12 |
| Google Scholar | 23 |
Marcinkiewicz integrals associated with Schrödinger operator and their commutators on vanishing generalized Morrey spaces