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| Decomposition of $L^{p}(\partial D_{a})$ Space andBoundary Value of Holomorphic Functions |
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Citation： |
Zhihong WEN,Guantie DENG,Cuiqiao WANG,Feifei QU.Decomposition of $L^{p}(\partial D_{a})$ Space andBoundary Value of Holomorphic Functions[J].Chinese Annals of Mathematics B,2017,38(5):1093~1110 |
| Page view： 2917
Net amount： 1213 |
Authors： |
Zhihong WEN; Guantie DENG;Cuiqiao WANG;Feifei QU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11271045) and the Higher School Doctoral
Foundation of China (No.20100003110004). |
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| Abstract： |
This paper deals with two topics mentioned in the title. First, it
is proved that function $f$ in $L^{p}(\partial D_{a})$ can be
decomposed into a sum $g+h$, where $D_{a}$ is an angular domain in
the complex plane, $g$ and $h$ are the non-tangential limits of
functions in $H^{p}(D_{a})$ and $H^{p}(\ov{D}_{a}^{c})$ in the sense
of $L^{p}(D_{a})$, respectively. Second, the sufficient and
necessary conditions between boundary values of holomorphic
functions and distributions in $n$-dimensional complex space are
obtained. |
Keywords： |
Hardy space, Rational function, Holomorphic function, Distribution |
Classification： |
32A10, 32A40, 36F20 |
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