Approximation of \((\psi, \beta)\)-differentiable functions of low smoothness by biharmonic Poisson integrals
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Publication:1760025
DOI10.1007/s11253-012-0616-2zbMath1263.31001OpenAlexW2116569521MaRDI QIDQ1760025
K. M. Zhyhallo, Yu. I. Kharkevych
Publication date: 23 November 2012
Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11253-012-0616-2
Approximation by operators (in particular, by integral operators) (41A35) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)
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On the approximation of the classes \(W_\beta^r H^\alpha\) by biharmonic Poisson integrals ⋮ On boundary values of three-harmonic Poisson integral on the boundary of a unit disk ⋮ Approximate characteristics of generalized Poisson operators on Zygmund classes ⋮ Approximation of classes \({C}_{\beta, \infty}^{\psi }\) by three-harmonic Poisson integrals in uniform metric (low smoothness) ⋮ Fourier transform of the summatory Abel-Poisson function ⋮ Some asymptotic properties of the solutions of Laplace equations in a unit disk ⋮ Approximation of the classes \(C_{\beta}^{\psi } H^\alpha\) by biharmonic Poisson integrals ⋮ Approximating properties of biharmonic Poisson integrals in the classes \(W_\beta^r H^\alpha\) ⋮ Approximating properties of biharmonic Poisson operators in the classes \(\widehat{L}_{\beta,1}^\psi\) ⋮ Approximation of the classes $W^{r}_{\beta,\infty}$ by three-harmonic Poisson integrals ⋮ Approximative properties of biharmonic Poisson integrals on Hölder classes ⋮ On some asymptotic properties of solutions to biharmonic equations
Cites Work
- Approximation of functions from the classes \(C_{\beta, \infty}^{\psi}\) by biharmonic Poisson integrals
- Approximation by triangular Fourier sums on classes of continuous periodic functions of two variables
- Approximation of conjugate differentiable functions by biharmonic Poisson integrals
- On the absolute summability of Fourier series of almost-periodic besicovitch functions
- Approximation of (ψ, β)-differentiable functions by Poisson integrals in the uniform metric
- On a biharmonic function in the unit disc
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