Lv Xiaofen
Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000 China.
J Inequal Appl. 2017;2017(1):286. doi: 10.1186/s13660-017-1560-3. Epub 2017 Nov 16.
Let be a real-valued plurisubharmonic function on [Formula: see text] whose complex Hessian has uniformly comparable eigenvalues, and let [Formula: see text] be the Fock space induced by . In this paper, we conclude that the Bergman projection is bounded from the th Lebesgue space [Formula: see text] to [Formula: see text] for [Formula: see text]. As a remark, we claim that Bergman projections are also well defined and bounded on Fock spaces [Formula: see text] with [Formula: see text]. We also obtain the estimates for the distance induced by and the [Formula: see text]-norm of Bergman kernel for [Formula: see text].
设(\varphi)是(\mathbb{C}^n)上的实值多重次调和函数，其复Hessian矩阵的特征值具有一致可比性，并且设(F^2_{\varphi})是由(\varphi)诱导的Fock空间。在本文中，我们得出对于(p\in(1,\infty))，Bergman投影从第(p)个Lebesgue空间(L^p(\mathbb{C}^n))到(F^2_{\varphi})是有界的。作为一个附注，我们声称对于(p\in(1,\infty))，Bergman投影在Fock空间(F^2_{\varphi})上也是定义良好且有界的。我们还得到了由(\varphi)诱导的距离以及(p\in(1,\infty))时Bergman核的(L^p)范数的估计。
