Mixed norm variable exponent Bergman space on the unit disc
Mixed norm variable exponent Bergman space on the unit disc
复制标题
单位圆盘上的混合范数变量指数伯格曼空间
DOI：
10.1080/17476933.2016.1140750
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发表时间：
2016
影响因子：
0.9
通讯作者：
S. Samko
中科院分区：
文献类型：
--
作者：
A. Karapetyants;S. Samko
我们介绍并研究了复平面上单位圆盘上的混合范数变阶Bergman空间。混合范数变量阶勒贝格型空间的定义是，要求函数 f 的傅里叶系数的变量指数范数序列属于 则定义为由解析函数组成的子空间。我们证明了伯格曼投影的有界性，并揭示了当从区间内部看时，此类空间的性质对变量指数 p(r) 的可能增长的依赖性。情况在 和 的情况下有很大不同。在这种情况下，我们还将引入的伯格曼空间刻画为来自 Hardy 空间的函数的 Hadamards 分数阶导数的空间。对这种情况进行了专门研究，并在这种情况下提出了一个开放问题。我们还揭示了当等距时以及当不再正确时 p(r) 增长率的条件。
We introduce and study the mixed norm variable order Bergman space on the unit disc in the complex plane. The mixed norm variable order Lebesgue-type space is defined by the requirement that the sequence of the variable exponent -norms of the Fourier coefficients of the function f belongs to Then is defined to be the subspace of which consists of analytic functions. We prove the boundedness of the Bergman projection and reveal the dependence of the nature of such spaces on possible growth of variable exponent p(r) when from inside the interval The situation is quite different in the cases and In the case we also characterize the introduced Bergman space as the space of Hadamards’s fractional derivatives of functions from the Hardy space The case is specially studied, and an open problem is formulated in this case. We also reveal the conditions on the rate of growth of p(r) when when isometrically, and when this is not longer true.