On nonlinear condensation principles with rates (Q1060367)

In this paper we extend our previous quantitative condensation principles to some nonlinear situations. More specifically, on the basis of the usual homogeneity, we are interested in some reductions of the additivity which will in particular enable us to treat condensation on arbitrary point sets. The usefulness of the general result is illustrated by some first applications concerned with the sharpness of error bounds for Fejér means on the quasi-normed spaces \(L^ q_{2\pi}\), \(0<q<1\), with Kolmogorov's example of an \(L^ 1_{2\pi}\)-function the trigonometric Fourier series of which diverges everywhere, and with the problem of nonequiconvergence.