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

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 M_α 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 V^γ(−Δ + V)^−β and V^γ∇(−Δ + V)^−β in the Lorentz-Morrey spaces , where the nonnegative potential V belongs to the reverse Hölder class B_∞(ℝⁿ).

Subject Classification:

• 42B20
• 42B35
• 47G10

Keywords:

• Maximal operator
• Fractional maximal operator
• Lorentz-Morrey spaces
• Bochner-Riesz operator
• Schrödinger-type operators