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

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