\textit{P. L. Butzer} and \textit{R. J. Nessel} [see ``Fourier analysis and approximation. Vol. 1: One-dimensional theory'' (1971; Zbl 0217.42603)] introduced the general method of summability, using a singular integral of the Fourier transform of a function \(\theta\), called \(\theta\)-summability. Special cases include many classical summability methods including the Bessel, Fejér, de la Vallée-Poussin, and Riesz means. The author already had some interesting results about Riesz means [\textit{F. Weisz}, Stud. Math. 131, No.~3, 253-270 (1998; Zbl 0934.42004)], and here considers their generalization to \(theta\) means. In addition to various estimates of the \(\theta\) means of a Fourier series and its conjugate series, in Hardy norms, \(L^p\) norms, and some mixed norm spaces, he also includes a long section where specific applications to the classical methods of summation are spelled out in detail. The scope is very broad, including even the tempered distribution case. This is a paper well worth reading.