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all records (17)

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30  Articles
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For odd r?Nr\in \mathbb{N}; a,ß>0\alpha, \beta >0; p?[1,8]p\in [1, \infty]; d?(0,2p)\delta \in (0, 2 \pi), any 2p2\pi-periodic function x?Lr8(I2p)x\in L^r_{\infty}(I_{2\pi}), I2p:=[0,2p]I_{2\pi}:=[0, 2\pi], and arbitrary measurable set B?I2p,B \subset ... see more

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

For any q>p>0q > p > 0, ?>0,\omega > 0, d=2?,d \ge 2 \omega,  we obtain the following sharp inequality of various metrics?x?Lq(Id)=?f+c?Lq(I2?)?f+c?Lp(I2?)?x?Lp(Id) \|x\|_{L_q(I_{d})} \le \frac{\|\varphi + c\|_{L_q(I_{2\omega})}}{\|\varphi +... see more

We obtain generalization of the known A.A. Ligun's inequality to non-normed LqL_q-spaces for derivatives of periodic functions.

We obtain the estimates of the seminorms of Weil of the functions on the real line and their derivatives with the help of local LpL_p-norms of the functions and uniform norms of their highest derivatives.

We prove the inequality that estimates seminorm of Weil of the derivatives of the functions on the real line with the help of uniform norm of the functions and their derivatives. We also solve the corresponding problem of Kolmogorov.

We establish sharp estimates of the LqL_q-norms on any finite interval for the polynomials and splines and their derivatives with the help of local LpL_p-norms of these polynomials and splines.

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