Pointwise $$\left( H,\Phi \right) $$H,Φ Strong Approximation by Fourier Series of $$L^{1}$$L1 Integrable Functions

Abstract

We will present an estimation of the generalized strong mean (H, Φ) as an approximation version of the Totik type generalization of the results of J. Marcinkiewicz and A. Zygmund on strong summability of Fourier series of integrable functions. As a measure of such approximation we will use the function constructed by function Ψ complementary to Φ on the base of definition of the Gabisoniya points. Some corollary and remark will also be given.Mathematics Subject Classification. 42A24.

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

“…as approximation version of the Totik type (see [14,15]) generalization of the mentioned results of J. Marcinkiewicz and A. Zygmund was obtained in [10] as follows:…”