On the diameters of some classes of analytic functions. I

In the spaces of analytic functionsE _q (), q1, introduced by V. I. Smirnov, where is a bounded simply connected domain in the plane with sufficiently smooth boundary , we obtain order estimates of diameters of the classesW ^r E _p () (p1, and r is a natural number 2) for distinct p and q.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 324–333, March, 1992.