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This work extends prior findings on Fourier series convergence in weighted spaces indicating broader implications for analysis.
The recent contribution by Gogoladze and Meskhia (Proc. A. Razmadze Math. Inst. 141:29–40, 2006) presents a generalization of classical results by Bernstein, Szász, Zygmund, and others on the absolute convergence of Fourier series with coefficients raised to a power ξ, analyzed via moduli of smoothness. In this work, we extend their findings to Fourier-Laplace series in the weighted function spaces Lₚ(σ ᵐ⁻¹), 1< p≤ 2, and we also establish the sharpness of our conditions when $p = 2$.
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Ouadih et al. (2026) studied this question.
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