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

Sharp Hardy's inequality for Jacobi and symmetrized Jacobi trigonometric expansions