INVERSE-THEOREMS IN LP FOR SOME MULTIDIMENSIONAL POSITIVE LINEAR-OPERATORS

Let {L(n)}n is-an-element-of N be positive linear operators in L(p)(I), I = [0, ] or [0, infinity). This paper considers their variants in L(p)(I x I) L(n,m)(F; x, y) = L(n)(F(u, v); y); x) = L(m)(F(u, v); x); y), n, m is-an-element-of N. The characterization problem for these operators is solved which gives the inverse theorems in L(p) for multidimensional Bernstein type operators.