Quantitative estimates of N.N. Luzin's C-property for classes of integrable functions

K. Oskolkow

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In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator $T : L^{p} (ℝ^{+}) \to L^{p} (ℝ^{+})$ defined by $(T f) (x) ≔ v (x) ʃ_{0}^{\infty} u (t) f (t) d t$ when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].

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