Multipliers for Jacobi expansions in the Hardy spaces

Journal of Inequalities and Applications

Zhong Xue¹  Zhongkai Li²  Yehao Shi³ 

[1] Department of Mathematics, Capital Normal University;Department of Mathematics, Shanghai Normal University;Elementary Education College, Capital Normal University;

关键词: Hardy space;    Multipliers;    Jacobi expansion;   

DOI  :  10.1186/s13660-020-2290-5

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown