Kolmogorov type inequalities for hypersingular integrals with sign-alternating characteristic

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
D.A. Levchenko (Oles Honchar Dnipropetrovsk National University)

Abstract


New sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of the form $$$\Omega(t) = \mathrm{sgn} \prod\limits_{k=1}^m t_k$$$ for multivariate functions from Hölder spaces are obtained.

Keywords


hypersingular integral; homogeneous characteristic; modulus of continuity

References


Arestov V.V. "Approximation of unbounded operators by the bounded ones and related extremum problems", Uspekhi mat. nauk, 1996; 51(6): pp. 88-124. (in Russian) doi:10.1070/RM1996v051n06ABEH003001

Babenko V.F. "On sharp inequalities of Kolmogorov type for bivariate functions", Dokl. NAN Ukrajiny, 2000; 5: pp. 7-11. (in Russian)

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)

Babenko V.F., Churilova M.S. "On inequalities of Kolmogorov type for derivatives of fractional order", Res. Math., 2001; 6: pp. 16-20. (in Russian)

Buslaev A.P., Tikhomirov V.M. "On inequalities for derivatives in multidimensional case", Mat. zametki, 1979; 25(1): pp. 59-74. (in Russian) doi:10.1007/BF01138146

Gejsberg S.P. "Generalization of Hadamard inequality", Researches on certain problems of constructive function theory: sb. nauch. tr. LOMI, Leningrad, 1965; 50: pp. 42-54. (in Russian)

Konovalov V.N. "Sharp inequalities for norms of functions, third partial and second mixed derivatives", Matem. zametki, 1978; 23(1): pp. 67-78. (in Russian) doi:10.1007/BF01104884

Samko S.G., Kilbas A.A., Marichev O.I. Integrals and derivatives of fractional order and their applications, Nauka i tekhnika, Minsk, 1987; 688 p. (in Russian)

Timoshin O.A. "Sharp inequalities between the derivatives of the second and third order", Dokl. RAN, 1995; 344(1): pp. 20-22. (in Russian)

Arestov V.V. "Inequalities for fractional derivatives on the half-line", Approximation theory: proc. conf., Warsaw, 1979; pp. 19-34.

Babenko V.F., Kofanov V.A., Pichugov S.A. "Multivariate inequalities of Kolmogorov type and their applications", Multivariate approximation and splines, Basel, 1997; pp. 1-12. doi:10.1007/978-3-0348-8871-4_1

Babenko V.F., Churilova M.S. "Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic", Banach J. Math., 2007; 1: pp. 66-77. doi:10.15352/bjma/1240321556




DOI: https://doi.org/10.15421/241003

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2010 V.F. Babenko, D.A. Levchenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU