We consider the Cauchy problem of second order hyperbolic equation with time depending coefficients. Time depending singular coefficient can bring some loss of regularity of the solution; for instance ``infinitely many oscillation'', ``infinite order degeneracy'' and ``accumulation of zeros'' crucially influence on the regularity loss. In this paper we make clear the order of regularity loss from the interaction of the singular effects, and also discuss the optimality.
"Loss of regularity for second order hyperbolic equations with singular coefficients." Osaka J. Math. 42 (4) 767 - 790, December 2005.