On The Constants For Landau's Type Inequalities

In this paper, we summary and study systematic the constants for Landau's Type Inequalities. In the Chapter1, we introduction the background and developing for Landau's Type Inequalities; In the Chapter2, we expand the constants for Landau's Type Inequalities vertically, in the C₀ -semigroups, C₀ contraction semigroups, groups, cosine functions and L_p-spaces, and prove them separately; In the Chapter3, we expand the constants for Landau's Type Inequalities horizontal, delimit the variable u in the higher derivatives as u∈D ( Aⁿ⁺¹ ); In the Chapter4, we apply the conclusion of the Riesz-Thorin interpolation theorem to prove the relationship of the constants for Landau's Type Inequalities.