ON A BESOV SPACE AND RADIAL LIMITS

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.

키워드

• radial limits;
• Besov space;

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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