Generalization of A.A. Ligun's inequality to $$$L_q$$$, $$$q \in [0, 1)$$$ spaces

V.A. Kofanov (Oles Honchar Dnipropetrovsk National University),


We obtain generalization of the known A.A. Ligun's inequality to non-normed $$$L_q$$$-spaces for derivatives of periodic functions.


Ligun A.A. "Inequalities for upper bounds of functionals", Analysis Math., 1976; 2(1): pp. 11-40. doi:10.1007/BF02079905

Kofanov V.A. "Inequalities for derivatives in $$$L_p$$$ spaces", Ukrainian Math. J., 2008; 60(10): pp. 1338-1349. (in Russian) doi:10.1007/s11253-009-0152-x

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, 1992; 304 p. (in Russian)

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on the infinite interval", Izbr. tr.: Matematika, mechanika, Moscow, 1985; pp. 252-263. (in Russian)

Hardy G.H., Littlewood J.E., Polya G. Inequalities, GIIL, Moscow, 1948; 456 p. (in Russian)

Tikhomirov V.M. "Set widths in functional spaces and theory of the best approximations", Uspekhi mat. nauk, 1960; 15(3): pp. 81-120. (in Russian) doi:10.1070/RM1960v015n03ABEH004093

Ligun A.A. "Sharp inequalities for spline-functions and the best quadrature formulas for certain classes of functions", Mat. zametki, 1976; 19(6): pp. 913-926. (in Russian) doi:10.1007/BF01149933

Babenko V.F., Korneichuk N.P., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, Kyiv, 2003; 590 p. (in Russian)




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