DOI QR코드

DOI QR Code

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

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.

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