  Four Jacobi settings are considered in the context of Hardy's inequality: the
trigonometric polynomials and functions, and the corresponding symmetrized
systems. In the polynomial cases sharp Hardy's inequality is proved for the
type parameters $\alpha,\beta\in(-1,\infty)^d$, whereas in the function systems
for $\alpha,\beta\in[-1/2,\infty)^d$. The ranges of these parameters are the
widest in which the corresponding orthonormal bases are composed of bounded
functions. Moreover, the sharp $L^1$-analogues of Hardy's inequality are
obtained with the same restrictions on the parameters $\alpha$ and $\beta$.
