an:03996415
Zbl 0615.46051
Guadalupe, Jos?? J.; Rezola, M. Luisa
The conjugate function in plane curves
EN
Can. Math. Bull. 31, No. 2, 147-152 (1988).
00165582
1988
j
46J15 30C20
rectifiable Jordan curve; normalized conformal mapping; BMO; boundedness of the conjugate function operator; quasiregular curves
Let \(\Gamma =\partial \Omega\) be a rectifiable Jordan curve and let \(\phi\) be the normalized conformal mapping from the unit disc D onto \(\Omega\). In this paper the conjugate function operator on \(\Gamma\) is defined in a natural way and the following result is obtained: ''The curves such that log \(| \phi '|\) belongs to the closure of \(L^{\infty}\) in BMO are exactly those for which the boundedness of the conjugate function operator is equivalent to the fact that \(w\in A_ p(\Gamma)''\). The quasiregular curves are examples of such curves.