Geodesic
On families of linear polynomial operators generated by Riesz kernels
Eurasian mathematical journal, Tome 1 (2010) no. 4, pp. 124-139

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Families of linear polynomial operators generated by the Riesz kernels are studied. Sharp ranges of convergence are found in many cases. It is shown that the approximation error is equivalent to the polynomial $K$-functional related to the apropricate power of the Laplace operator, if the family converges. 
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     author = {K. Runovski and H.-J. Schmeisser},
     title = {On families of linear polynomial operators generated by {Riesz} kernels},
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K. Runovski; H.-J. Schmeisser. On families of linear polynomial operators generated by Riesz kernels. Eurasian mathematical journal, Tome 1 (2010) no. 4, pp. 124-139. http://geodesic.mathdoc.fr/item/EMJ_2010_1_4_a6/