| Abstract: | One constructs a new linear bounded operator which solves the problem of free interpolation in the Hardy space H . This operator is analogous to the well-known interpolation operator of P. W. Jones. One of the fundamental distinctions of the operator constructed in this paper consists in the fact that it acts in the smallest (in a certain sense) linear closed subspace of the space H which, in turn, gives the possibility to obtain new results on free interpolation for several subclasses of the spaces H. In the second part of the paper one proves a theorem which, in a significant number of cases, allows us to reduce the solution of the problem on multiple interpolation (when the multiplicities are bounded in their totality) to the problem of free interpolation with simple nodes. One gives several examples of the application of this theorem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 35–46, 1983. |
