Annales Academić Scientiarum Fennicć
Mathematica
Volumen 36, 2011, 291-300

HARDY SPACES AND UNBOUNDED QUASIDISKS

Yong Chan Kim and Toshiyuki Sugawa

Yeungnam University, Department of Mathematics Education
214-1 Daedong Gyongsan 712-749, Korea; kimyc 'at' ynu.ac.kr

Tohoku University, Division of Mathematics, Graduate School of Information Sciences
Aoba-ku, Sendai 980-8579, Japan; sugawa 'at' math.is.tohoku.ac.jp

Abstract. We study the maximal number 0 \le h \le +\infty for a given plane domain \Omega such that f \in H^p whenever p < h and f is analytic in the unit disk with values in \Omega. One of our main contributions is an estimate of h for unbounded K-quasidisks.

2000 Mathematics Subject Classification: Primary 30H10; Secondary 30C50, 46E15.

Key words: Hardy space, harmonic measure, quasiconformal mapping.

Reference to this article: Y.C. Kim and T. Sugawa: Hardy spaces and unbounded quasidisks. Ann. Acad. Sci. Fenn. Math. 36 (2011), 291-300.

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doi:10.5186/aasfm.2011.3618