Multipliers for Jacobi expansions in the Hardy spaces

The purpose of the paper is to study the coefficient multipliers of the Hardy spaces $H^{p}$ associated with Jacobi expansions of exponential type. The main results are about the boundedness from $H^{p}$ to $\ell ^{q}$ of the multiplier operators in terms of Jacobi expansions of exponential type for (i) $p=1$, $2\le q<\infty $; (ii) $\gamma ( \alpha ,\beta )^{-1}< p<1\le q<\infty $, under appropriate conditions, where $\gamma (\alpha ,\beta )\in (1,\infty ]$ is a number depending on the parameters of the Jacobi system.