I'm reading Demailly's 'Complex Analytic and Algebraic Geometry' on page 145. Let $K$ be a compact set and $\Theta$ be a positive current of order $0$ of bidimension $(p,p)$ and $\beta = dd^c|z|^2$. Then, he claims there are constants $C_i$ such that $$C_1\|\Theta\|_K\leq \int_K\Theta\wedge\beta^p\leq C_2\|\Theta\|_K$$
My Question:
How to get this inequality?(Especially the left part)
In general, do we have the Cauchy-like inequality for differential forms? i.e. $|\int\alpha\wedge\beta|\leq \int|\alpha\wedge\beta|\leq \|\alpha\|\|\beta\|$. I don't even know how to define the norm in a proper way.
