Commutator of fractional integral with Lipschitz functions associated with Schrödinger operator on local generalized Morrey spaces
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV
Kirsehir Ahi Evran University, Türkiye
Prof. Dr. Ali AKBULUT
Kırşehir Ahi Evran Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Boundary Value Problems (Q4) | ||
| Dergi ISSN | 1687-2762 | ||
| Dergi Tarandığı Indeksler | SCI | ||
| Makale Dili | Türkçe | Basım Tarihi | 05-2018 |
| Cilt / Sayı / Sayfa | 2018 / 1 / – | DOI | 10.1186/s13661-018-1002-2 |
| Makale Linki | http://dx.doi.org/10.1186/s13661-018-1002-2 | ||
| Özet |
| Let L = -Delta + V be a Schrodinger operator on R-n, where n >= 3 and the nonnegative potential V belongs to the reverse Holder class RHq1 for some q(1) > n/2. Let b belong to a new Campanato space Lambda(theta)(nu) (rho) and I-beta(L) 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 local generalized Morrey spaces LM rho,phi alpha,V,{x0} generalized Morrey spaces M-rho,phi(alpha,V) and vanishing generalized Morrey spaces VM rho,phi alpha,V associated with Schrodinger operator, respectively. When b belongs to Lambda(theta)(nu) (rho) with theta > 0, 0 < nu < 1 and (phi(1),phi(2)) satisfies some conditions, we show that the commutator operator [b,I-beta(L)] are bounded from LM rho,phi 1 alpha,V,{x0} to LM rho,phi 2 alpha,V,{x0} from LMq,phi 1 alpha,V to VMq,phi 2 alpha,V and from VM rho,phi 1 alpha,V to VM rho,phi 2 alpha,V, 1/p - 1/q = ( beta +nu)/n. |
| Anahtar Kelimeler |
| Schrodinger operator | Fractional integral | Commutator | Lipschitz function | Local generalized Morrey space |