Powers of quasi-Banach lattices and orthogonally additive polynomials

The paper aims to examine convexity and concavity conditions for homogeneous orthogonally additive polynomials in quasi-Banach lattices. We characterize (p,q)-convex quasi-Banach lattice by the property that every positive orthogonally additive polynomial defined on such lattice is (p,q)-convex as well as obtain some versions of Krivine factorization result and Grothendieck's inequality for orthogonally additive polynomials in quasi-Banach lattices.