Singular values of compact pseudodifferential operators of variable order with nonsmooth symbol

We consider compact pseudodifferential operators with symbols whose decaying order with respect to the variable $\xi$ depends on the space variable. We obtain the estimates for singular values as well as validity conditions of the Weyl's asymptotics. The results are formulated in terms of the symbol belonging to the classes of multipliers of integral operators. We give applications of the results to the $L_2$ - small ball deviation asymptotics for Gaussian processes with variable Hurst parameter.