= Radial homotopy operator
{title2=$H\alpha=\int_0^1\rho_t^*(\iota_R\alpha)\,dt/t$}
On a star-shaped domain, let $\rho_t(x)=tx$ and $R=\sum x_j\partial_{x_j}$. On positive-degree <differential forms>, $H\alpha=\int_0^1\rho_t^*(\iota_R\alpha)\,dt/t$ satisfies $dH+Hd=\mathrm{id}-\rho_0^*$. It gives a primitive of every closed positive-degree form. On a star-shaped domain in a complex vector space, contraction with the two type components of $R$ shows that $H$ sends type $(p,q)$ into $(p-1,q)\oplus(p,q-1)$. There is no primitive assertion for a nonzero constant function.
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