Maximal and Fractional maximal operators in the Lorentz-Morrey spaces and their applications to the Bochner-Riesz and Schrödinger-type operators


KÜÇÜKASLAN A.

Journal of Interdisciplinary Mathematics, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1080/09720502.2021.1885817
  • Journal Name: Journal of Interdisciplinary Mathematics
  • Journal Indexes: Emerging Sources Citation Index, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts

Abstract

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 Ma 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 Schrodinger type operators in the Lorentz Morrey spaces, where the nonnegative potential V belongs to the reverse Holder class.