On convergence of singular integral operators with radial kernels. (English) Zbl 1325.45017

Fasshauer, Gregory E. (ed.) et al., Approximation theory XIV: San Antonio 2013. Selected papers based on the presentations at the international conference, San Antonio, TX, USA, April 7–10, 2013. Cham: Springer (ISBN 978-3-319-06403-1/hbk; 978-3-319-06404-8/ebook). Springer Proceedings in Mathematics & Statistics 83, 295-308 (2014).
Summary: In this paper, we prove the pointwise convergence of the operator \(L(f;x,y;\lambda)\) to the function \(f(x_0,y_0)\), as \((x,y;\lambda)\) tends to \((x_0,y_0;\lambda _0)\) by the three parameter family of singular integral operators in \(L_1(Q_1)\), where \(Q_1\) is a closed, semi-closed, or open rectangular region \(<-a\), \(a>\times <-b\), \(b\). Here, the kernel function is radial and we take the point \((x_0,y_0)\) as a \(\mu\)-generalized Lebesgue point of \(f\).
For the entire collection see [Zbl 1291.65003].


45P05 Integral operators
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