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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (2): 211-216    DOI:
    
The estimation of $L^p$ norm of the Berezin-type transform
ZHOU Li-fang, LU Jin
Dept. of Math., Huzhou University, Huzhou 313000, China
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Abstract  Berezin-type transform plays an important role in the study of the $(\alpha, \beta)$-hamonicity of the functions. The boundeness and the exact upper-norm and lower-norm of the Berezin-type transform on $L^p(1<p\leq\infty)$ space are given by using the hypergeometric function and Schur's test.

Key words： Berezin-type transform      operator norm      hypergeometric functions     
Received: 19 February 2014      Published: 05 June 2018
CLC:  O174.56  
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ZHOU Li-fang
LU Jin
Cite this article:

ZHOU Li-fang, LU Jin. The estimation of $L^p$ norm of the Berezin-type transform. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 211-216.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I2/211


Berezin型变换的$L^p$范数估计

Berezin型变换在研究函数的$(\alpha, \beta)$-调和性问题中起到了关键的作用. 利用超几何函数和Schur检验, 证明了Berezin型变换在$L^p(1<p\leq\infty)$空间上是有界的, 并给出了其范数的精确上下界.

关键词： Berezin型变换,  算子范数,  超几何函数 
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