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On Maximal Regularity and Semivariation of α-Times Resolvent Families*
Department of Mathematics, Sichuan University, Chengdu, China
Department of Mathematics, Sichuan University, Chengdu, China
- 1 Department of Mathematics, Sichuan University, Chengdu, China
- 2 Department of Mathematics, Sichuan University, Chengdu, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 680–684·Published 27 November 2013·DOI10.4236/apm.2013.38091
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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 .
Keywordsα-Times Resolvent FamilyMaximal RegularitySemivariation
- 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
- 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
- E. G. Bajlekova, “Fractional Evolution Equations in Banach Spaces,” Dissertation, Eindhoven University of Technology, 2001.
- C. S. Honig, “Volterra Stieltjes Integral Equations,” NorthHolland, Amsterdam, 1975.
- A. Pazy, “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer, New York, 1983.