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The aim of this work is to give sufficient conditions ensuring that the space  PAP (,  X ,  µ ) of  µ -pseudo almost periodic functions and the space  PAA (,  X ,  µ ) of  µ -pseudo almost automorphic functions are invariant by the convolution product  f  =  k  *  f ,  k ∈ L  1 (). These results establish sufficient assumptions on  k  and the measure  µ . As a consequence, we investigate the existence and uniqueness of  µ -pseudo almost periodic solutions and  µ -pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations.

Convolutions in µ -pseudo almost periodic and µ -pseudo almost automorphic function spaces and applications to solve Integral equations