On Maximal Regularity and Semivariation of α-Times Resolvent Families*
نویسندگان
چکیده
Let and A be the generator of an -times resolvent family 1 α < < 2 α ( ) { } 0 t S t α ≥ on a Banach space X. It is shown that the fractional Cauchy problem , ( ) ( ) ( ) t u t Au t f t α = + D ( ] 0, t r ∈ ; has maximal regularity on ( ) ( 0 , u u′ ) ( ) 0 D A ∈ [ ] ( 0, ; C r ) X if and only if is of bounded semivariation on ( ) ⋅ Sα [ ] 0, r .
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