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The Carleson measure and meromorphic functions of uniformly bounded characteristic
1991
Annales Academiae Scientiarum Fennicae Series A I Mathematica
For a meromorphic function /(z) defined in the unit disc D : lzl < 1 on the complex z-plane, z = x * iy, we denote its spherical derivative bv f#(r) and introduce the differentiable form dpyQ) = (1 -lzl2)lf+(z)l2dxdy. We prove that f(z) has the uniformly bounded characteristic if and only if the measur" WQ) is the Carleson measure. This result answers a question posed by S. Yamashita in Internat.
doi:10.5186/aasfm.1991.1619
fatcat:ib7fd2uzurcypkfcukybfecchq