Abstract
This paper deals with two topics mentioned in the title. First, it is proved that function f in L p(∂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 \({H^p}\left( {\overline D _a^c} \right)\) 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.
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The authors are very grateful to the referee for the insightful comments and suggestions, which greatly improved the exposition of the manuscript.
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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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Wen, Z., Deng, G., Wang, C. et al. Decomposition of L p(∂D a ) space and boundary value of holomorphic functions. Chin. Ann. Math. Ser. B 38, 1093–1110 (2017). https://doi.org/10.1007/s11401-017-1025-5
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DOI: https://doi.org/10.1007/s11401-017-1025-5