Li, Guoquan; Lu, Shanzhen On the linearization of the Carleson operator. (Chinese. English summary) Zbl 1135.42304 J. Beijing Norm. Univ., Nat. Sci. 42, No. 4, 358-361 (2006). Summary: The following theorem be obtained that the Carleson operator \(\mathcal C\) is of the weak \((p,q)\) type if and only if there exists constant a \(A>0\) such that the following estimate \(\| {\mathcal C}_n f \| _{L(q,\infty)} \leq A\| f\|_p\) holds for all bounded functions \(n:\mathbb{R}\to \mathbb{R}\), which is an infinite (or finite) linear combination of characteristic functions of intervals. Here, \({\mathcal C}_n\) is the linearization of \(\mathcal C\) at \(n\). MSC: 42A20 Convergence and absolute convergence of Fourier and trigonometric series 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 47B33 Linear composition operators 46E99 Linear function spaces and their duals PDFBibTeX XMLCite \textit{G. Li} and \textit{S. Lu}, J. Beijing Norm. Univ., Nat. Sci. 42, No. 4, 358--361 (2006; Zbl 1135.42304)