In this paper, we continue the study of new weighted spaces of holomorphic functions on the unit disc with the mixed norm defined in terms of conditions on Fourier coefficients of a function. Here we present the case in which the corresponding conditions are related to grand and small Lebesgues spaces, i.e. the Fourier coefficients as functions of radial variable belong to either grand or small space, and the norms of these coefficients taken in the corresponding space all together form a $l^q$ sequence. We provide the characterization of functions in such mixed norm spaces and study the boundedness of the holomorphic projection.

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关于混合范数全纯大空间和小空间

在本文中，我们继续研究单位圆上全纯函数的新加权空间，其中混合范数根据函数的傅立叶系数条件定义。这里我们给出对应条件与大勒贝格空间和小勒贝格空间有关的情况，即作为径向变量的函数的傅里叶系数属于大空间或小空间，这些系数在对应空间中取的范数共同形成一种$l^q$顺序。我们在这种混合范数空间中提供函数的表征，并研究全纯投影的有界性。