Results 61 to 70 of about 106 (83)

Landau-kolmogorov-hörmander inequalities on the semiaxis

Mathematical Notes, 1999
The problem of the asymmetric ideal spline least deviating from zero in the \(C[a,b]\)-metric is solved. The authors prove the Landau-Kolmogorov-Hörmander inequalities for the norms of positive and negative parts of intermediate derivatives of functions on the semiaxis that take into account restrictions on the positive and negative part of the higher ...
V F Babenko, V A Kofanov, S A Pichugov
exaly   +3 more sources

One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

Ukrainian Mathematical Journal, 2019
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V F Babenko, Babenko V F
exaly   +3 more sources

Landau-Kolmogorov and Related Inequalities

1991
Let f be a real function with n derivatives on an interval I of the real line. Define $${M_k}(p,I) = \parallel {f^{(k)}}{\parallel _p},\quad 0 \leqslant k \leqslant n.$$
D. S. Mitrinović   +2 more
openaire   +1 more source

Multivariate Landau–Kolmogorov-type inequality

Mathematical Proceedings of the Cambridge Philosophical Society, 1989
AbstractAssuming that the nth iterate of the Laplacian Δnf belongs to L∞(ℝ), we show for 0 < k < 2n thatwhere ∂/∂ξi is the derivative in the ei direction. The result is also extended to other Banach spaces of functions on ℝd.
openaire   +1 more source

Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment

Ukrainian Mathematical Journal, 2001
For arbitrary \(t\in [0,1]\), \(p\in [1,\infty ]\) and \(A\geq 2\) the author finds the best possible constant \(B\) in the inequality \[ |x'(t)|\leq A\|x\|_{L_\infty [0,1]}+B\|x''\|_{L_p(0,1)}. \] This leads to the precise inequality for the norms \[ \|x'\|_\infty \leq \frac{2}{h}\|x\|_\infty +\left( \frac{h}{p'+1}\right)^{1/p'}\|x''\|_p \] valid for ...
openaire   +2 more sources

On Inequalities of the Landau–Kolmogorov–Hörmander Type on a Segment and Real Straight Line

Ukrainian Mathematical Journal, 2000
We prove inequalities of the Landau–Kolmogorov–Hormander type for the uniform norms (on some subinterval) of positive and negative parts of intermediate derivatives of functions defined on a finite interval. By using the limit transition, we obtain a new proof or the well-known Hormander result.
openaire   +1 more source

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