On some correlations in the theory of degenerate semigroups of operators

In the theory of degenerate operator semigroups the notions of (L, p)-radial and strongly (L, p)-radial operators have essential significances. In this work it is shown that in certain situations every of them means a generalisation in the case of degenerate strongly continouos semigroups of Hille-Yosida conditions on an infinitesimal generator of (С0)-continuous semigroup. Besides, sufficient conditions of equivalence of these notions are obtained. Analogous results are established for (L, p)-sectorial and strongly (L, p)-sectorial operators in the case of degenerate strongly holomorphic semigroups.