A note on the theorems of Paley and Stein
The author gives an estimate of the Lorentz norm of a function in terms of its Fourier coefficients with respect to an orthonormal system \(\{\varphi_n\}\) on \([0,1 ]\), where \(\varphi_n\in\text{BMO}\), and the BMO-seminorm \(\|\varphi_n\|_*\) is bounded. The results generalize the classical theorems by Paley and Stein, and also refine the estimates proposed by \textit{V. I. Kolyada} [Math. Notes, 51, No. 3, 235-244 (1992); translation from Mat. Zametki 51, No. 3, 24-34 (1992; Zbl 0791.42019)].
scientific article; zbMATH DE number 1631379