Singular numbers of the imbedding operators for certain classes of analytic and harmonic functions (Q1093042)

Let G and g be bounded simply connected domains whose boundaries are rectifiable Jordan curves and \(\bar g\subset G\). Let \(\lambda\),\(\mu\) be finite Borel measures defined on \(\bar G\) and \(\bar g,\) respectively. By \(A^ 2(G,\lambda)\) (respectively: \(h^ 2(G,\lambda))\) is denoted the closure in \(L^ 2(G,\lambda)\) of all functions analytic (resp. harmonic) in G. There is studied the best approximation in the mean of functions under consideration by estimations of s-numbers of embedding operators \[ I: A^ 2(G,\lambda)\to L_ 2(g,\mu),\quad I f=f|_ g, \] \[ I_ h: h^ 2(G,\lambda)\to L_ 2(g,\mu),\quad I_ hf=f|_ g, \] provided that they are compact. Remark of the reviewer: The language of the paper seems to be rather strange: it is a so-called dictionary translation (for instance: ``circumstance'' instead of ``neighbourhood'').