Cover Image

On Kolmogorov-type inequalities for fractional derivatives of functions of two variables

We prove a new exact Kolmogorov-type inequality estimating the norm of a mixed fractional-order derivative (in Marchaud's sense) of a function of two variables via the norm of the function and the norms of its partial derivatives of the first order.

Saved in:

Bibliographic Details
Date:	2008
Main Authors:	Babenko, V. F., Pichugov, S. A., Бабенко, В. Ф., Пичугов, С. А.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 2008
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3200
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Kolmogorov-type inequalities for mixed derivatives of functions of many variables
by: Babenko, V. F., et al.
Published: (2004)

On Kolmogorov-Type Inequalities with Integrable Highest Derivative
by: Babenko, V. F., et al.
Published: (2002)

One inequality of the Landau – Kolmogorov type for periodic functions of two variable
by: Babenko, V. F., et al.
Published: (2019)

Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions
by: Babenko, V. F., et al.
Published: (2010)

Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation
by: Babenko, V. F., et al.
Published: (2002)

Exact Kolmogorov-Type Inequalities with Bounded Leading Derivative in the Case of Low Smoothness
by: Babenko, V. F., et al.
Published: (2001)

Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions
by: Babenko, V.F., et al.
Published: (2010)

Comparison of exact constants in Kolmogorov-type inequalities for periodic and nonperiodic functions of many variables
by: Babenko, V. F., et al.
Published: (2006)

On Kolmogorov-type inequalities for functions defined on a semiaxis
by: Babenko, V. F., et al.
Published: (2007)

One inequality of the Landau–Kolmogorov type for periodic functions of two variable
by: V. F. Babenko
Published: (2019)

Kolmogorov-Type Inequalities for Fractional Derivatives on the Half Line
by: Levchenko, D. A., et al.
Published: (2014)

On the connection between certain inequalities of the Kolmogorov type for periodic and nonperiodic functions
by: Babenko, V. F., et al.
Published: (1999)

Kolmogorov-Type Inequalities for Fractional Derivatives on the Half Line
by: D. A. Levchenko
Published: (2014)

On additive inequalities for intermediate derivatives of functions given on a finite interval
by: Babenko, V. F., et al.
Published: (1997)

Exact inequalities for derivatives of functions of low smoothness defined on an axis and a semiaxis
by: Babenko, V. F., et al.
Published: (2006)

Comparison of Exact Constants in Inequalities for Derivatives of Functions Defined on the Real Axis and a Circle
by: Babenko, V. F., et al.
Published: (2003)

Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment
by: Babenko, Yu. V., et al.
Published: (2001)

On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net
by: Babenko, V. F., et al.
Published: (1997)

Inequality of the Bernshtein type for polynomial splines in the space $L_2$
by: Babenko , V. F., et al.
Published: (1991)

On inequalities for norms of intermediate derivatives on a finite interval
by: Babenko, V. F., et al.
Published: (1995)

Kolmogorov type inequalities for norms of fractional derivatives of functions defined on the positive half-line
by: O. Kozynenko, et al.
Published: (2020)

Kolmogorov type inequalities for norms of fractional derivatives of functions defined on the positive half-line
by: Kozynenko, O., et al.
Published: (2020)

Kolmogorov inequalities for the norms of the Riesz derivatives of functions of many variables
by: N. V. Parfinovych
Published: (2017)

Some sharp Landau-Kolmogorov–Nagy-type inequalities in Sobolev spaces of multivariate functions
by: Babenko, V., et al.
Published: (2023)

Nikol’skii – Stechkin-type inequalities for the increments of trigonometric polynomials in metric spaces
by: Pichugov, S. A., et al.
Published: (2017)

Investigations of dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications
by: Babenko, V. F., et al.
Published: (2000)

Approximation of continuous vector functions
by: Babenko, V. F., et al.
Published: (1994)

On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives
by: Kofanov, V. A., et al.
Published: (2003)

On the set of extremal functions in certain Kolmogorov-type inequalities
by: Kofanov, V. A., et al.
Published: (2004)

Inequalities for trigonometric polynomials in spaces with integral metric
by: Pichugov, S. A., et al.
Published: (2011)

On sharp Kolmogorov-type inequalities taking into account the number of sign changes of derivatives
by: Kofanov, V. A., et al.
Published: (2008)

On correlation between sharp Kolmogorov type inequalities and sharp Kolmogorov–Remez type inequalities
by: Kofanov, V. A., et al.
Published: (2021)

On correlation between sharp Kolmogorov type inequalities and sharp Kolmogorov–Remez type inequalities
by: V. O. Kofanov
Published: (2021)

Inequalities for upper bounds of functionals on the classes $W^r H^{ω}$ and their applications
by: Babenko, V. F., et al.
Published: (2000)

Optimization of approximate integration of monotone functions of two variables
by: Babenko, V. F., et al.
Published: (1999)

Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications
by: Babenko, V. F., et al.
Published: (2011)

Approximation of measurable periodic functions in measure by step functions
by: Pichugov, S. A., et al.
Published: (1996)

Bernstein-type inequalities for $\mathcal{L}$-splines
by: Babenko, V. F., et al.
Published: (1993)

Some Bernstein-type inequalities for trigonometric polynomials
by: Babenko, V. F., et al.
Published: (1993)

On exact constants in inequalities for norms of derivatives on a finite segment
by: Babenko, V. F., et al.
Published: (1999)