Generalized absolute convergence of series of Fourier coefficients with respect to Haar type systems (Q1746434)

Orthogonal systems of Haar type introduced by Vilenkin are studied. The authors investigate the convergence of the series \(\sum_{n=1}^{\infty} \gamma_n | \widehat{f}(n)|^{\beta}\) with weighted sequences \((\gamma_n)\) from the Gogoladze-Meskhi classes and functions \(f\) from \(L^{p}[0,1]\) and the Wiener space \(V^{p}[0,1]\), \(p \geq 1\). Sufficient conditions for the convergence are expressed in terms of best approximations. The sharpness of the results is also shown.