A Landau-Kolmogorov inequality for generators of families of bounded operators

作者：Lizama Carlos^*; Miana Pedro J

来源：Journal of Mathematical Analysis and Applications, 2010, 371(2): 614-623.

DOI：10.1016/j.jmaa.2010.05.065

• Landau-Kolmogorov inequality
• Integrated semigroups
• Integrated cosine functions
• Abstract differential equations

A Landau-Kolmogorov type inequality for generators of a wide class of strongly continuous families of bounded and linear operators defined on a Banach space is shown Our approach allows us to recover (in a unified way) known results about uniformly bounded C(0)-semigroups and cosine functions as well as to prove new results for other families of operators. In particular, if A is the generator of an alpha-times integrated family of bounded and linear operators arising from the well-posedness of fractional differential equations of order beta+ 1 then, we prove that the inequality parallel to Ax parallel to(2) <= 8M(2

• 出版日期2010-11-15