Two-weight norm inequalities on Morrey spaces

A description of all the admissible weights similar to the Muckenhoupt class $A_p$ is an open problem for the weighted Morrey spaces. In this paper necessary condition and sufficient condition for two-weight norm inequalities on Morrey spaces to hold are given for the Hardy-Littlewood maximal operator. Necessary and sufficient condition is also verified for the power weights

The Fatou property of block spaces

Around thirty years ago, block spaces, which are the predual of Morrey spaces, had been considered. However, it seems that there is no proof that block spaces satisfy the Fatou property. In this paper the Fatou property for block spaces is verified and the predual of block spaces is characterized