We introduce 2-microlocal Morrey type Besov and Triebel-Lizorkin spaces with variable exponents give some characterizations of these by so-called Peetre?s maximal functions. The atomic molecular decompositions are obtained. Finally, using decomposition the property local means, we get wavelet spaces.

We define a Muckenhoup-type condition on weighted Morrey spaces using the Köthe dual of space. show that is necessary and sufficient for boundedness maximal operator defined with balls centered at origin spaces. A modified characterizes inequalities Calderón operator. also local usual Hardy–Littlewood operator, simplifying previous characterization Nakamura–Sawano–Tanaka. For same in case globa...