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4.112  Articles
1 of 412 pages  |  10  records  |  more records»
We obtain the strengthened Kolmogorov comparison theorem in asymmetric case.In particular, it gives us the opportunity to obtain the following strengthened Kolmogorov inequality in the asymmetric case:?x(k)±?8=?fr-k(·;a,ß)±?8E0(fr(·;a,ß))1-k/r8|||x|||1-k/... see more

In this article we prove sharp Landau-Kolmogorov type inequalities on a class of charges defined on Lebesgue measurable subsets of a cone in Rd\mathbb{R}^d, d?1d\geqslant 1, that are absolutely continuous with respect to the Lebesgue measure. In addition ... see more

We obtain new sharp inequality of Kolmogorov type for differentiable periodic functions x?L31x \in L_1^3.

We obtain new sharp Kolmogorov type inequalities, estimating the norm of mixed Marchaud type derivative of multivariate function through the C-norm of function itself and its norms in Hölder spaces.

We obtained sharp inequalities of Kolmogorov type for non-periodic functions on the real domain. The obtained results were applied to solve some extremum problems for non-periodic functions and splines on the real domain.

We prove two generalizations of Kashin-Besov inequality for fractional derivatives. The corollaries of proved theorems are some analogues of Paly theorem, which allow to give lower bounds for polynomials by orthogonal systems in Lp[0,1]L_p [0, 1] spaces f... see more

We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Harnack inequality and a strong maximum principle.

We prove new sharp inequality of Kolmogorov type that estimates the norm of mixed fractional Marchaud derivative of n-variable function by C-norm of this function and its norms in Lipschitz spaces.

We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Harnack inequality and a strong maximum principle.

1 of 412 pages  |  10  records  |  more records»