On maximal regularity and semivariation of α-times resolvent families

2010/07/26 by Fu-Bo Li, Miao Li, Li, Fu-Bo +1
Mathematics · #34G10 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 45N05 #Secondary 26A33 #math.FA #msc:26A33 #msc:34G10 #msc:45N05

paper · pdf · doi:10.48550/arxiv.1007.4455

7 pages

arxiv created 2010/07/26 · arxiv updated 2010/07/27

Abstract

Let 1< α<2 and A be the generator of an α-times resolvent family \S_α(t)\_{t ≥ 0} on a Banach space X. It is shown that the fractional Cauchy problem \bf D_t^αu(t) = Au(t)+f(t), t ∈ [0,r]; u(0), u'(0) ∈ D(A) has maximal regularity on C([0,r];X) if and only if S_α(⋅) is of bounded semivariation on [0,r].

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