On Maximal Regularity and Semivariation of α-Times Resolvent Families*
ABSTRACT
Let 
and A be the generator of an 
-times resolvent family 
on a Banach space X. It is shown that
the fractional Cauchy problem 
has maximal regularity on 
if and only if 
is of bounded semivariation on 
.
Cite this paper
F. Li and M. Li, "On Maximal Regularity and Semivariation of α-Times Resolvent Families*," Advances in Pure Mathematics, Vol. 3 No. 8, 2013, pp. 680-684. doi: 10.4236/apm.2013.38091.
F. Li and M. Li, "On Maximal Regularity and Semivariation of α-Times Resolvent Families*," Advances in Pure Mathematics, Vol. 3 No. 8, 2013, pp. 680-684. doi: 10.4236/apm.2013.38091.
References
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http://dx.doi.org/10.1090/S0002-9939-1981-0612734-2 [2] D. K. Chyan, S. Y. Shaw and S. Piskarev, “On Maximal Regularity and Semivariation of Cosine Operator Functions,” Journal London Mathematical Society, Vol. 59, No. 3, 1999, pp. 1023-1032.
http://dx.doi.org/10.1112/S0024610799007073 [3] E. G. Bajlekova, “Fractional Evolution Equations in Banach Spaces,” Dissertation, Eindhoven University of Technology, 2001. [4] C. S. Honig, “Volterra Stieltjes Integral Equations,” NorthHolland, Amsterdam, 1975. [5] A. Pazy, “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer, New York, 1983.
[1] C. C. Travis, “Differentiability of Weak Solutions to an Abstract Inhomogeneous Differential Equation,” Proceedings of the American Mathematical Society, Vol. 82, 1981, pp. 425-430.
http://dx.doi.org/10.1090/S0002-9939-1981-0612734-2 [2] D. K. Chyan, S. Y. Shaw and S. Piskarev, “On Maximal Regularity and Semivariation of Cosine Operator Functions,” Journal London Mathematical Society, Vol. 59, No. 3, 1999, pp. 1023-1032.
http://dx.doi.org/10.1112/S0024610799007073 [3] E. G. Bajlekova, “Fractional Evolution Equations in Banach Spaces,” Dissertation, Eindhoven University of Technology, 2001. [4] C. S. Honig, “Volterra Stieltjes Integral Equations,” NorthHolland, Amsterdam, 1975. [5] A. Pazy, “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer, New York, 1983.