Marcinkiewicz integrals associated with Schrödinger operator and its commutators on generalized Morrey spaces
Yazarlar (3)
Prof. Dr. Ali AKBULUT Kırşehir Ahi Evran Üniversitesi, Türkiye
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
Mehriban N. Omarova Azerbaijan National Academy of Sciences, Azerbaycan
Bildiri Türü Açık Erişim Tebliğ/Bildiri Bildiri Dili İngilizce
Bildiri Alt Türü Özet Metin Olarak Yayınlanan Tebliğ (Uluslararası Kongre/Sempozyum)
Bildiri Niteliği Alanında Hakemli Uluslararası Kongre/Sempozyum
DOI Numarası 10.1186/s13661-017-0851-4
Kongre Adı ” The VI Congress of the Turkic World Mathematical Society (TWMS 2017), Astana, Kazakhstan
Kongre Tarihi 02-10-2017 / 05-10-2017
Basıldığı Ülke Kazakistan Basıldığı Şehir Astana
UAK Araştırma Alanları
Matematiksel Analiz
Özet
Let L= − Δ + V be a Schrödinger operator, where Δ is the Laplacian on Rn and the non-negative potential V belongs to the reverse Hölder class RHq for q≥ n/ 2. In this paper, we study the boundedness of the Marcinkiewicz integral operators μjL and their commutators [b,μjL] with b∈ BMOθ(ρ) on generalized Morrey spaces Mp,φα,V(Rn) associated with Schrödinger operator and vanishing generalized Morrey spaces VMp,φα,V(Rn) associated with Schrödinger operator. We find the sufficient conditions on the pair (φ1, φ2) which ensure the boundedness of the operators μjL from one vanishing generalized Morrey space VMp,V to another VMp,V, 1 < p< ∞ and from the space VM1,V to the weak space VWM1,V. When b belongs to BMOθ(ρ) and (φ1, φ2) satisfies some conditions, we also show that [b,μjL] is bounded from Mp,V to Mp,V and from VMp,V to VMp,V, 1 < p< ∞.
Anahtar Kelimeler
BMO | commutator | Marcinkiewicz integral | Schrödinger operator | vanishing generalized Morrey space