arXiv subjects
Publications and source records attributed to Gabdolla Akishev.
This article considers the Lipschitz space with mixed logarithmic smoothness of $2\pi$ periodic functions of several variables. We obtain equivalent descriptions of the norm of the Lipschitz space and prove embedding theorems between Besov and Lipschitz spaces.
The article considers the Lorentz space $L_{p,τ}(\mathbb{T}^{m})$, $2π$ of periodic functions of many variables and $S_{p,τ,θ}^{0, \overline{b}}\mathbf{B}$, $S_{p, τ, θ}^{0, \overline{b}}B$ -- spaces of functions with mixed logarithmic smoothness. The article establishes necessary and sufficient conditions for embedding the spaces $S_{p, τ, θ}^{0, \overline{b}}\mathbf{B}$ and $S_{p, τ, θ}^{ 0, \overline{b}}B$ into each other.
In this paper we consider anisotropic Lorentz-Karamata space $2π$ of periodic functions of $m$ variables and Nikol'skii--Besov's class . In this paper, we establish order-sharp estimates of the best approximation by trigonometric polynomials with harmonic numbers from the step hyperbolic cross of functions from the Nikol'skii - Besov class in the norm of the anisotropic Lorentz-Karamata space.
In this paper we consider $L_{\overline{p}, \overline\alpha, \overline{\tau}}^{*}(\mathbb{T}^{m})$ anisotropic Lorentz-Zyg\-mu\-nd space $ 2\pi$ of periodic functions of $m$ variables and Nikol'skii--Besov's class $S_{\overline{p}, \overline\alpha, \overline{\tau}, \bar{\theta}}^{\bar r}B$. In this paper, we establish order-sharp estimates of the best approximation by trigonometric polynomials with harmonic numbers from the step hyperbolic cross of functions from the Nikol'skii - Besov class in the norm of the anisotropic Lorentz-Zygmund space.
In this paper we consider $ X(\bar\varphi)$ anisotropic symmetric space $ 2\pi$ of periodic functions of $m$ variables, in particular, the generalized Lorentz space $L_{\bar{\psi},\bar{\tau}}^{*}(\mathbb{T}^{m})$ and Nikol'skii--Besov's class $S_{X(\bar{\varphi}),\bar{\theta}}^{\bar r}B$. The article proves an embedding theorem for the Nikol'skii - Besov class in the generalized Lorentz space and establishes an upper bound for the best approximations by trigonometric polynomials with harmonic numbers from the hyperbolic cross of functions from the class $S_{X(\bar{\varphi}),\bar{\theta}}^{\bar r}B$.