Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications

2012 ◽  
Vol 277 (S1) ◽  
pp. 9-20
Author(s):  
V. F. Babenko ◽  
N. V. Parfinovich
Keyword(s):  
Multivariate Functions ◽  
Kolmogorov Type ◽  
Derivatives Of

scholarly journals Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions

2010 ◽  
Vol 62 (3) ◽  
pp. 343-357 ◽  
Author(s):  
V. F. Babenko ◽  
N.V. Parfinovych ◽  
S. A. Pichugov
Keyword(s):  
Fractional Derivatives ◽  
Multivariate Functions ◽  
Kolmogorov Type ◽  
Derivatives Of

Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications

2012 ◽  
Vol 187 (1) ◽  
pp. 9-21
Author(s):  
Vladislav F. Babenko ◽  
Natal’ya V. Parfinovich
Keyword(s):  
Multivariate Functions ◽  
Kolmogorov Type ◽  
Derivatives Of

scholarly journals On inequalities of Kolmogorov type for fractional Hadamard derivatives of functions defined on the half-line

2021 ◽  
Vol 17 ◽  
pp. 31
Author(s):  
V.F. Babenko ◽  
N.V. Parfinovich
Keyword(s):  
Half Line ◽  
Kolmogorov Type ◽  
Derivatives Of

New exact inequalities for Hadamard fraction derivatives of functions, defined on the half-line, are obtained.

scholarly journals Estimates of the norms of Riesz derivatives of multivariate functions

2017 ◽  
Vol 22 (1(29)) ◽  
pp. 46-61
Author(s):  
Н. В. Парфінович
Keyword(s):  
Multivariate Functions ◽  
Derivatives Of

scholarly journals PROPERTIES OF INTEGRALS WHICH HAVE THE TYPE OF DERIVATIVES OF VOLUME POTENTIALS FOR DEGENERATED $\overrightarrow{2\lowercase{b}}$ - PARABOLIC EQUATION OF KOLMOGOROV TYPE

2021 ◽  
Vol 9 (2) ◽  
pp. 7-21
Author(s):  
V. Dron' ◽  
I. Medyns'kyi
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Homogeneous Equation ◽  
Hölder Spaces ◽  
Kolmogorov Type ◽  
Estimates Of Solutions ◽  
The Cauchy Problem ◽  
The Given ◽  
Holder Spaces ◽  
Derivatives Of

In weight Holder spaces it is studied the smoothness of integrals, which have the structure and properties of derivatives of volume potentials which generated by fundamental solution of the Cauchy problem for degenerated $\overrightarrow{2b}$-parabolic equation of Kolmogorov type. The coefficients in this equation depend only on the time variable. Special distances and norms are used for constructing of the weight Holder spaces. The results of the paper can be used for establishing of the correct solvability of the Cauchy problem and estimates of solutions of the given non-homogeneous equation in corresponding weight Holder spaces.

scholarly journals On inequalities of Kolmogorov type for fractional derivatives of functions defined on the real domain

2021 ◽  
Vol 16 ◽  
pp. 28
Author(s):  
V.F. Babenko ◽  
M.S. Churilova
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Kolmogorov Type ◽  
The Real ◽  
Higher Derivative ◽  
Real Domain ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
New Inequalities

We obtain new inequalities that generalize known result of Geisberg, which was obtained for fractional Marchaud derivatives, to the case of higher derivatives, at that the fractional derivative is a Riesz one. The inequality with second higher derivative is sharp.

scholarly journals Exact inequalities of Kolmogorov type for Hadamard fractional derivatives of functions defined on half-line

2021 ◽  
Vol 18 ◽  
pp. 38
Author(s):  
V.F. Babenko ◽  
N.V. Parfinovich
Keyword(s):  
Fractional Derivatives ◽  
Half Line ◽  
Kolmogorov Type ◽  
Derivatives Of

New exact inequalities for Hadamard fractional derivatives of functions, defined on the half-line, are obtained.

scholarly journals Kolmogorov type inequalities for hypersingular integrals with sign-alternating characteristic

2021 ◽  
Vol 18 ◽  
pp. 18
Author(s):  
V.F. Babenko ◽  
D.A. Levchenko
Keyword(s):  
Multivariate Functions ◽  
Hölder Spaces ◽  
Kolmogorov Type ◽  
Hypersingular Integrals ◽  
Holder Spaces

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.

Kolmogorov-type inequalities for norms of Riesz derivatives of functions of several variables with Laplacian bounded in L ∞ and related problems

2014 ◽  
Vol 95 (1-2) ◽  
pp. 3-14 ◽  
Author(s):  
V. F. Babenko ◽  
N. V. Parfinovich ◽  
S. A. Pichugov
Keyword(s):  
Kolmogorov Type ◽  
Several Variables ◽  
Derivatives Of
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