On the Cesàro means of conjugate Jacobi series
The author continues his studies on conjugate Jacobi series and conjugate functions [see J. Approximation Theory 86, No. 2, 179-196 (1996; Zbl 0859.42018)]. He obtains exact estimates of the norm of the conjugate \((C,\delta)\) kernel for \(0\leq\delta\leq\alpha+ 1/2\). Main results: In the case \(\varepsilon>\alpha+ 1/2\) the \((C,\delta)\) means of the conjugate Jacobi expansion of a function \(f\in L_{\alpha\beta}\), where \(\alpha\geq \beta\geq -1/2\), converge to the Jacobi conjugate function \(\widetilde f\) almost everywhere. The convergence of the \((C,\alpha+ 1/2)\) means at the critical index is also deduced by means of an equiconvergence theorem.
scientific article; zbMATH DE number 1076155