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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.
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 $E_M (G)$.
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) $.
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.