The weighted kernels of Szegoe type were introduced systematically in 1950 by Nehari in order to solve a number of extremal problems. He pointed out many of the relationships among the weighted kernels and the well known domain functions, and proposed a problem (called the Nehari problem) for the weighted Garabedian kernel. This problem has been investigated by constructing a class W_0 of the weight functions, In 1956 Ozawa derived an interesting result for the holomorphic part of the Garabedian kernel. In the present paper, a generalization of Ozawa's result for the weighted Garabedian kernel will be given and the weighted Szegoe kernel will be examined in terms of the zeros of its n th derivative. Furthermore, an attempt will be made to solve the Nehari problem from a general angle.
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