Weighted Morrey spaces

In this chapter, the authors examine the boundedness of linear and sublinear operators in weighted Morrey spaces and weighted local Morrey spaces. There are mainly two types of weighted Morrey spaces. In 2008, Natasha Samko defined weighted Morrey spaces of Samko-type and in 2009 Komori(-Furuya) and Shirai defined weighted Morrey spaces of Komori–Shirai-type. The authors consider the boundedness of the maximal operator local weighted Morrey spaces of Komori–Shirai-type. The ranges obtained in Propositions 167 and 168 are the same as those for weighted Morrey spaces of Komori–Shirai-type and those for weighted Morrey spaces of Samko-type, respectively. Many researchers investigated the boundedness properties of the linear operators acting on weighted Morrey spaces. Weighted Morrey spaces emerged a little later than generalized Morrey spaces. In fact, in 2008 and 2009, two papers on weighted Morrey spaces appeared. Komori-Furuya and Shirai investigated weighted Morrey spaces mainly in connection with the boundedness of operators.