Pointwise Multipliers on Weak Morrey Spaces

Abstract

We consider generalized weak Morrey spaces with variable growth condition on spaces of homogeneous type and characterize the pointwise multipliers from a generalized weak Morrey space to another one. The set of all pointwise multipliers from a weak Lebesgue space to another one is also a weak Lebesgue space. However, we point out that the weak Morrey spaces do not always have this property just as the Morrey spaces not always.

Keywords

• morrey space
• weak morrey space
• pointwise multiplier
• 42b35
• 46e30