On Kolmogorov-Type Inequalities with Integrable Highest Derivative
We obtain the new exact Kolmogorov-type inequality \| x^( k ) \|_2 K\| x \|_2^r - k - 1 / 1 2 . - ulldelimiterspace 2 r - 1 / 1 2 . - ulldelimiterspace 2 \| x^( r ) \|_1^kr - 1 / - 1 2 . - ulldelimiterspace 2 for 2π-periodic functions \(x L_1^r\) and any k, r ∈ N, k < r. We present applications of this inequality to problems of approximation of one class of functions by another class and estimates of K-functional type., number=12, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Babenko, V. F. and Kofanov, V. A. and Pichugov, S. A., year=2002, month=Dec., pages=1694–1697