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arXiv · 1405.3993

Approximation of conjugate functions by general linear operators of their Fourier series at the Lebesgue points

Wlodzimierz Lenski·Bogdan Szal
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Abstract

The pointwise estimates of the deviations $\widetilde{T}_{n,A,B}^{\text{}%}f\left(\cdot \right) -\widetilde{f}(\cdot)$ and $\widetilde{T}_{n,A,B}^{% \text{}}f\left(\cdot \right) -\widetilde{f}(\cdot,\varepsilon)$ in terms of moduli of continuity $\widetilde{\bar{w}}_{\cdot}f$ and $\widetilde{w}%_{\cdot}f$ are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal.

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Wlodzimierz Lenski, Bogdan Szal. 2014-05-15. Approximation of conjugate functions by general linear operators of their Fourier series at the Lebesgue points. https://arxiv.org/abs/1405.3993

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