Gromov symplectic width and Hofer-Zehnder symplectic capacity of the classical domains of four types

The symplectic capacities are important invariant in the study of symplectic topology and Hamiltonian dynamics. However, their computations and estimations are difficult. In this paper, we calculate and estimate the Gromov symplectic width and Hofer-Zehnder symplectic capacity of the classical domains of four types which play important roles in the theory of functions of several complex variables and complex geometry. This will be very useful to the further study of the classical domains.