Some Extensions of the Kolmogorov–Stein Inequality

Ha Huy Bang1, Vu Nhat Huy2
1Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam
2Department of Mathematics, College of Science, Vietnam National University, Hanoi, Vietnam

Tóm tắt

Từ khóa


Tài liệu tham khảo

Bang, H.H.: A remark on the Kolmogorov–Stein inequality. J. Math. Anal. Appl. 203, 861–867 (1996)

Bang, H.H.: On an inequality of Bohr for Orlicz spaces. Bull. Pol. Acad. Sci. 49, 383–389 (2001)

Bang, H.H., Thu, M.T.: On a Landau–Kolmogorov inequality. J. Inequal. Appl. 7, 663–672 (2002)

Bohr, H.: Ein allgemeiner Satz über die Integration eines trigonometrischen Polynoms. Prace Matem. -Fiz. 43, 273–288 (1935)

Bojanov, B.D., Varma, A.K.: On a polynomial inequality of Kolmogorov type. Proc. Amer. Math. Soc. 124, 491–496 (1996)

Borwein, P., Erdélyi, T.: Polynomials and Polynomial Inequalities. Graduate Texts in Mathematics, vol. 161. Springer-Verlag, New York (1995)

Burenkov, V.I.: Exact constants in inequalities for norms of intermediate derivatives on a finite interval. Proc. Steklov Inst. Math. 156, 22–29 (1980)

Certain, M.W., Kurtz, T.G.: Landau–Kolmogorov inequalities for semigroups and groups. Proc. Amer. Math. Soc. 63, 226–230 (1977)

Chernov, P.R.: Optimal Landau–Kolmogorov inequalities for dissipative operators in Hilbert and Banach spaces. Adv. Math. 34, 137–144 (1979)

Ditzian, Z.: Some remarks on inequalities of Landau and Kolmogorov. Aequat. Math. 12, 145–151 (1975)

Ditzian, Z.: A Kolmogorov-type inequality. Math. Proc. Camb. Philos. Soc. 136, 657–663 (2004)

Favard, J.: Application de la formule sommatoire d’Euler ` la démonstration de quelques propriétés extrémales des intégrales des fonctions périodiques et presque-périodiques. Mat. Tidsskr. B, 81–94 (1936)

Hörmander, L.: A new generalization of an inequality of Bohr. Math. Scand. 2, 33–45 (1954)

Kofanov, V.A.: On sharp Kolmogorov-type inequalities taking into account the number of sign changes of derivatives. Ukr. Math. J. 55, 548–565 (2008)

Kolmogorov, A.N.: On inequalities between upper bounds of the successive derivatives of an arbitrary function on an infinite interval. Amer. Math. Soc. Transl. Ser. 1 2, 233–243 (1962)

Krasnoselskii, M.A., Rutickii, Y.B.: Convex functions and orlicz spaces. GITTL, Moscow (1958). Engl. Transl. Noordhoff (1961)

Luxemburg, W.: Banach function spaces. (Thesis). Technische Hogeschool te Delft., The Netherlands (1955)

Nikolskii, S.M.: Approximation of functions of several variables and imbedding theorems. Moscow, Nauka (1977)

Rao, M.M., Ren, Z.D.: Theory of Orlicz spaces. Marcel Dekker, New York (1991)

Stein, E.M.: Functions of exponential type. Ann. Math. 65, 582–592 (1957)

Tikhomirov, V.M., Magaril-Il’jaev, G.G.: Inequalities for derivatives. In Kolmogorov, A.N. Selected Papers, pp 387–390. Moscow, Nauka (1985)

Trigub, R.M.: Comparison of linear differential operators. Math. Notes 82, 380–394 (2007)