  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.
