A DESCRIPTION OF HANKEL OPERATORS OF CLASS \mathfrak{S}_p FOR p>0, AN INVESTIGATION OF THE RATE OF RATIONAL APPROXIMATION, AND OTHER APPLICATIONS

The main result is the following description of Hankel operators in the Schatten-von Neumann class when : where is the Hankel operator with symbol , and is the Besov class. This result extends results obtained earlier for by the author to the case . Also described are the Hankel operators in the Schatten-Lorentz classes , , . Precise descriptions of classes of functions defined in terms of rational approximation in the bounded mean oscillation norm are given as an application, along with a complete investigation of the case where the decrease is of power order, and some precise results on rational approximation in the -norm. Certain other applications are also considered.Bibliography: 57 titles.

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