Summability of Multi-Dimensional Trigonometric Fourier Series

Understand

We consider the summability of one- and multi-dimensional trigonometric Fourier series.

• The Fej{\'e}r and Riesz summability methods are investigated in detail.
• Different types of summation and convergence are considered.
• We will prove that the maximal operator of the summability means is bounded from the Hardy space $H_p$ to $L_p$, for all $p>p_0$, where $p_0$ depends on the summability method and the dimension.