Whitney constants and approximation of m-quasi-linear forms by m-linear forms

We discuss some relations between Whitney constants wm(BX,Y) for bounded functions from, the unit ball of a real normed space X into another real normed space Y. In particular, we generalize a result of Tsar'kov thatwml(BX,Y)∼n(m-1)/2for X=l2nand for anyYto any n-dimensional X (here wml denotes linearized Whitney constant).