Comparison of Exact Constants in Inequalities for Derivatives of Functions Defined on the Real Axis and a Circle

Kolmogorov-type inequalities for mixed derivatives of functions of many variables

“…It was shown in [13] that, in the case where a Kolmogorov-type inequality holds for nonperiodic functions defined on the entire number axis, the exact constant in this inequality does not exceed the exact constant in an analogous inequality for periodic functions. More exactly, let…”

Comparison of exact constants in Kolmogorov-type inequalities for periodic and nonperiodic functions of many variables

“…Relations between the exact constants (2) in inequalities of the type (2) for periodic and nonperiodic functions defined on the real axis were established in [10]. Namely, it was proved that…”

“…Note that, in the proof of Theorem 1, we essentially use the one-dimensional scheme (see [10]). First, we present several auxiliary statements.…”