Pointwise (H, Φ) Strong Approximation by Fourier Series of LΨ Integrable Functions


  • Włodzimierz Łenski University of Zielona Góra




Strong approximation, rate of pointwise strong summability, Orlicz spaces


We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H, Φ) as an approximation version of the Totik type generaliza- tion of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from LΨ. As a measure of such approximation we will use the function constructed by function Ψ com- plementary to Φ on the base of definition of the LΨ points. Some corollary and remarks will also be given.


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How to Cite

Łenski, W. (2021). Pointwise (H, Φ) Strong Approximation by Fourier Series of LΨ Integrable Functions. Tamkang Journal of Mathematics, 53(1), 1-9. https://doi.org/10.5556/j.tkjm.53.2022.3219