Estimates for absolutely summing norms of polynomials and multilinear maps (Q2716943)

In the introduction the authors compile results containing lower bounds for the usual norms of scalar-valued multilinear mappings and homogeneous polynomials on \(\ell_p\) or \(c_0\) using sums of values of the canonical basis vectors. NEWLINENEWLINENEWLINEIn the following paragraphs new results concerning the usual and absolutely \((r;p_1, \ldots , p_n)\)-summing norms of vector-valued multilinear mappings and homogeneous polynomials are given which unify and extend the former theorems. NEWLINENEWLINENEWLINEIn the last paragraph the authors consider image spaces with cotype \(q\). They give estimates of absolutely \((q,1)\)-summing norms of multilinear mappings and homogeneous polynomials in terms of the cotype constant and and the usual norms. Moreover, absolutely \((q,1)\)-summing entire mappings are treated.