## Doubly-weighted pseudo almost periodic functions.(English)Zbl 1247.42008

Inspired by the weighted Morrey spaces, the author introduces and studies a new class of functions called doubly-weighted pseudo-almost periodic functions (respectively, doubly-weighted pseudo-almost automorphic functions), which generalizes in a natural fashion weighted pseudo-almost periodic functions (respectively, weighted pseudo-almost automorphy). In addition to the above, the author also introduces the class of doubly-weighted pseudo-almost periodic functions of order $$k$$ (respectively, doubly-weighted pseudo-almost automorphic functions of order $$k$$), where $$k$$ is in $$(0,1)$$. The stability of the convolution, translation invariance, existence of a doubly-weighted mean for almost periodic functions, and a composition result are studied.

### MSC:

 42A75 Classical almost periodic functions, mean periodic functions 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
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