Marcinkiewicz integrals associated with Schrödinger operator and their commutators on vanishing generalized Morrey spaces
Yazarlar (3)
Prof. Dr. Ali AKBULUT
Kırşehir Ahi Evran Üniversitesi, Türkiye
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Azerbaijan National Academy Of Sciences, Azerbaycan
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Boundary Value Problems | ||
| Dergi ISSN | 1687-2762 | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 08-2017 |
| Cilt / Sayı / Sayfa | 2017 / 1 / – | DOI | 10.1186/s13661-017-0851-4 |
| Makale Linki | https://boundaryvalueproblems.springeropen.com/track/pdf/10.1186/s13661-017-0851-4 | ||
| 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 |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 14 |
| SCOPUS | 12 |
| Google Scholar | 22 |