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42  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 consider a free boundary problem of incompressible viscous flow governing the motion of an isolated liquid mass. The liquid is subjected to capillary forces at the boundary and the coefficient of the surface tension depends on the temperature satisfyin... 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.

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