2021/08/15 by Abdulhamit Kucukaslan, Abdülhamit Küçükaslan
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Operator theory #Physics #Pure mathematics #Quantum mechanics #Type (biology) #math.FA #msc:42B20 #msc:42B35 #msc:47G10
paper · pdf · doi:10.1080/09720502.2021.1885817
openalex publication_date 2021/08/15 · openalex created_date 2021/08/30 · arxiv created 2021/11/05 · arxiv updated 2021/11/09 · openalex updated_date 2026/08/05
The aim of this paper is to obtain boundedness conditions for the maximal function Mf and to prove the necessary and sufficient conditions for the fractional maximal oparator Mα in the Lorentz-Morrey spaces which are a new class of functions. We get our main results by using the obtained sharp rearrangement estimates. The obtained results are applied to the boundedness of particular operators such as the Bochner-Riesz operator and the Schrödinger-type operators Vγ(−Δ + V)−β and Vγ∇(−Δ + V)−β in the Lorentz-Morrey spaces , where the nonnegative potential V belongs to the reverse Hölder class B∞(ℝn).