On the Kähler form of complex \(L^{p}\) space and its Lagrangian subspaces (Q2352169)

The author studies the complex \(L^p\) plane, which is equipped with the complex \(L^p\) norm \[ F_p(z,w) = ||(z,w)||_p := (|z|^p + |w|^p)^\frac{1}{p}, \] for \(1\leq p < \infty\). First, the Kähler form is computed associated to the complex \(L^p\) spaces and then the author describes the set of Lagrangian subspaces of \(\mathbb{C}^2\) with complex \(L^p\) norm.