Rational function approximation of Hardy space on half strip

ABSTRACT

In this paper, through appropriate rational approximation, we prove that a function f in $L^p(\partial I_a)$, with particular interest in the index range $1\le p<\infty ,$ can be decomposed into a sum $g+h$ in the sense of $L^p(\partial I_a)$, where $I_a$ is a half strip domain in the complex plane, g and h are the non-tangential limits of functions in $H^p(I_a)$ and $H^p({\overline{I}}_a^c)$, respectively. For the case $0<p<1,$ we show that a rational function in $L^p(\partial I_a)$ can be decomposed into a sum of rational functions in $H(I_a)$ and $H({\overline{I}}_a^c)$.

KEYWORDS:

• Hardy space
• rational function approximation
• half strip domain

AMS SUBJECT CLASSIFICATIONS:

• 32A10
• 36F20

Acknowledgements

The authors are very grateful to the anonymous referees for their insightful comments and many valuable suggestions, which greatly improved the exposition of the manuscript. The first author was supported by the Natural Science Foundation of Colleges of Jiangsu Province [no. 17KJD110002], and the Foundation Project of Jiangsu Normal University [no. 16XLR033]. The second author was supported by the National Natural Science Foundation of China [no. 11271045] and the Higher School Doctoral Foundation of China [no. 20100003110004].

Notes

No potential conflict of interest was reported by the authors.