Mathematics

CLC number: O174.5

A Note of the Interpolating Sequence in Q_p∩H^∞

School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, Anhui, China

Received: 26 August 2023

Abstract

In this paper, ${\left\{z_n\right\}}_{n=\mathrm{1}}^{\mathrm{\infty }}$ acts as an interpolating sequence for $Q_p\bigcap H^{\mathrm{\infty }}$. An analytic function f is constructed, and $f(z_n)={\sum }_j{\lambda }_j{f}_{z_j}(z_n)={\lambda }_n,n=\mathrm{1,2},\cdots$ for any $\left\{{\lambda }_n\right\}\in l^{\mathrm{\infty }}$, where f and $f_{z_j}$ belong to $Q_p\bigcap H^{\mathrm{\infty }}$. As a result, the study achieves a comparable outcome for $F\left(p,p-\mathrm{2},s\right)\bigcap H^{\mathrm{\infty }}$.