Multipliers for Jacobi expansions in the Hardy spaces

Abstract

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

Keywords

• Hardy space
• Multipliers
• Jacobi expansion