Let 1 p < 1 and let μ be a finite positive Borel measure on the unit diskD. The area Nevanlinna-Lebesgue spaceNp(μ) consists of allmeasurable functions h on D such that log+ |h| 2 Lp(μ), and the area Nevanlinna space Np is the subspace consisting of all holomorphic functions, in Np((1 |z|2)d(z)), where > 1 and is area measure onD. We characterize Carleson measures for Np , defined to be those measures μ for which Np Np(μ). As an application, we show that the spaces Np are closed under both differentiation and integration. This is in contrast to the classical Nevanlinna space, defined by integration on circles centered at the origin, which is closed under neither. Applications to composition operators and to integral operators are also given.
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机译：令1 p <1并使μ为单位diskD上的有限正Borel度量。面积Nevanlinna-Lebesgue空间Np（μ）由D上的所有可测量函数h组成，使得log + | h | 2 Lp（μ），面积Nevanlinna空间Np是由所有全纯函数组成的子空间，在Np（（1 | z | 2）d（z））中，其中> 1并且是D上的面积度量。我们表征了Np的Carleson测度，定义为Np Np（μ）的那些测度μ。作为一个应用，我们证明了空间Np在微分和积分下都是封闭的。这与经典的Nevanlinna空间形成了鲜明对比，Nevanlinna空间是通过以原点为中心的圆上的积分来定义的，该圆在两个原点下均不闭合。还给出了对合成算子和积分算子的应用。
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