Polyharmonic Bergman spaces and Bargmann type transforms

详细信息    查看全文

• 作者：Luí ; s V. Pessoa ; ¹ ; ^{luis.pessoa@tecnico.ulisboa.pt} ; Ana Moura Santos ; ¹ ; ^{ana.moura.santos@tecnico.ulisboa.pt}
• 关键词：Beurling&ndash ; Alhfors transform ; Bargmann type transform ; Harmonic components ; Kernel functions ; Polyharmonic Bergman space
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：619-641
• 全文大小：460 K
• 卷排序：449

文摘

In the main result of the paper we prove the decomposition of polyharmonic Bergman spaces over the upper-half plane into spaces of polyanalytic functions. Then, we introduce the decomposition of polyharmonic Bergman spaces into the orthogonal sum of its true polyharmonic Bergman subspaces and we state isometric isomorphisms between the different true polyharmonic Bergman spaces. This allows us to define the k-th harmonic Hilbert component of a polyharmonic Bergman function and to prove closed formulas for the reproducing kernel functions of the true polyharmonic and the polyharmonic Bergman spaces. The harmonic complex Fourier transform is introduced in order to give an explicit description of the cartesian and the Laguerre harmonic components of the images of a Bargmann type transform for the true polyharmonic Bergman spaces. Finally, it is proved that the polyharmonic Bergman space of order j is isometric isomorphic to 2j copies of the corresponding Hardy space.