Tensorial representation of p-regular multilinear operators between Banach lattices

We introduce the new class of the (p;p(1),...,p(m))-regular multilinear operators between Banach lattices, that is defined using a summability property that provides the multilinear version of the (p, q)-regular operators. Some composition results are proved and we show that every continuous multilinear operators are (p;p(1),...,p(m))-regular under some requirements. We find the trace duality representation of this class of multilinear operators by presenting a reasonable crossnorm that satisfies that the topological dual space of an (m+1)-fold tensor product is isometric to the space of (p;p(1),...,p(m))-regular multilinear operators.