Marcinkiewicz integrals associated with Schrodinger operator and their commutators on vanishing generalized Morrey spaces

AKBULUT, ALİ; GULIYEV, VAGIF; Omarova, Mehriban N.

doi:10.1186/s13661-017-0851-4

Marcinkiewicz integrals associated with Schrodinger 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

Mehriban N. Omarova Azerbaijan National Academy Of Sciences, Azerbaycan

Makale Türü	Diğer (Teknik, not, yorum, vaka takdimi, editöre mektup, özet, kitap krıtiği, araştırma notu, bilirkişi raporu ve benzeri) (Uluslararası alan indekslerindeki dergilerde yayınlanan teknik not, editöre mektup, tartışma, vaka takdimi ve özet türünden makale)
Dergi Adı	Boundary Value Problems
Dergi ISSN	1687-2762
Makale Dili	İngilizce	Basım Tarihi	08-2017
Cilt / Sayı / Sayfa	2017 / 1 / –	DOI	10.1186/s13661-017-0851-4
UAK Araştırma Alanları

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

BM Sürdürülebilir Kalkınma Amaçları

Atıf Sayıları
Web of Science	14
Scopus	12

Marcinkiewicz integrals associated with Schrodinger operator and their commutators on vanishing generalized Morrey spaces

Marcinkiewicz integrals associated with Schrodinger operator and their commutators on vanishing generalized Morrey spaces

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