Approximation of conjugate functions by general linear operators of their Fourier series at the Lebesgue points. (English) Zbl 1306.42008
Summary: Pointwise estimates of the deviations \(\tilde{T}_{n,A,B}f(\cdot)-\tilde{f}(\cdot)\) and \(\tilde{T}_{n,A,B}f(\cdot)-\tilde{f}(\cdot,\varepsilon)\) in terms of the moduli of continuity \(\tilde{\bar{\omega}}.f\) and \(\tilde{\omega}.f\) are proved. Analogous results on norm approximation with remarks and a corollary are also given. These results generalize a theorem of M. L. Mittal [J. Math. Anal. Appl. 220, No. 2, 434–450 (1998; Zbl 0917.42006)].
MSC:
| 42A50 | Conjugate functions, conjugate series, singular integrals |
| 42A24 | Summability and absolute summability of Fourier and trigonometric series |
Keywords:
conjugate functions; Fourier series; summability; rate of approximation; Lebesgue points; moduli of continuityCitations:
Zbl 0917.42006References:
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