대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제24권4호
  • /
  • Pages.561-564
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  • 2009
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON A BESOV SPACE AND RADIAL LIMITS

  • Kim, Pil-Lan (DEPARTMENT OF MATHEMATICS EDUCATION ANDONG NATIONAL UNIVERSITY) ;
  • Kwon, Ern-Gun (DEPARTMENT OF MATHEMATICS EDUCATION ANDONG NATIONAL UNIVERSITY) ;
  • Park, Jong-Hee (DEPARTMENT OF MATHEMATICS EDUCATION ANDONG NATIONAL UNIVERSITY)
  • 발행 : 2009.10.31
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초록

A holomorphic function space in the unit disc D satisfying $\int_D|f'(z)|^p(1-|z|^2)^{p-1}dA(z)$<$\infty$ is quite close to $H^p$. The problems on the existence of the radial limits are considered for this space. It is proved that the situation for p > 2 is totally different from the situation for p $\leq$ 2.

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참고문헌

  1. P. L. Duren, Theory of Hp Spaces, Academic Press, New York, 1970
  2. C. N. Kellog, An extension of the Hausdorff-Young theorem, Michigan Math. J. 18 (1971), 121–127 https://doi.org/10.1307/mmj/1029000635
  3. E. G. Kwon, A note on the coefficients of mixed normed spaces, Bull. Austral. Math. Soc. 33 (1986), 253–260 https://doi.org/10.1017/S0004972700003129
  4. A. Zygmund, Trigonometric Series, Cambridge University Press, London, 1959