Local products as operators

It is shown for a large class of domains that the bilinear forms associated with formal expressions of the type ${\mathrm{\int h(x)a}}_{s_p}^{\mathrm{\hspace{0.17em}†}}{\mathrm{(x).\dots a}}_{s_1}^{\mathrm{\hspace{0.17em}†}}{\mathrm{(x)a}}_{t_1}{\mathrm{(x)\dots a}}_{t_q}\mathrm{(x)dx}$ define closable operators if and only if p, qε{0, 1}.