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Approximation by Means of Fourier Trigonometric Series in Weighted Orlicz Spaces
Guven,Israfilov 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.2
The order of approximation of Cesaro, Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the modulus of continuity in re‡exive weighted Orlicz spaces with Muckenhoupt weights. These results were applied to estimate the rate of approximation of Cesaro, Zygmund and Abel sums of Faber series in weighted Smirnov-Orlicz classes de…ned on simply connected domains of the complex plane.
APPROXIMATION BY INTERPOLATING POLYNOMIALS IN SMIRNOV-ORLICZ CLASS
Akgun Ramazan,Israfilov Daniyal M. Korean Mathematical Society 2006 대한수학회지 Vol.43 No.2
Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.
MULTIPLIER THEOREMS IN WEIGHTED SMIRNOV SPACES
Guven, Ali,Israfilov, Daniyal M. Korean Mathematical Society 2008 대한수학회지 Vol.45 No.6
The analogues of Marcinkiewicz multiplier theorem and Littlewood-Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve.
Multiplier theorems in weighted Smirnov spaces
Ali Guven,Daniyal M. Israfilov 대한수학회 2008 대한수학회지 Vol.45 No.6
The analogues of Marcinkiewicz multiplier theorem and Littlewood- Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve. The analogues of Marcinkiewicz multiplier theorem and Littlewood- Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve.
Approximation by interpolating polynomials in Smirnov-Orlicz class
Ramazan Akg\,Daniyal M. Israfilov 대한수학회 2006 대한수학회지 Vol.43 No.2
Let $\Gamma $ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let $G:=\operatorname{int}\Gamma $. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_{n}$ for $\overline{G}$ to the function of the reflexive Smirnov-Orlicz class $E_{M}\left( G\right) $ is equivalent to the best approximating polynomial rate in $E_{M}\left( G\right) $.