刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:15 January 2017
年:2017
卷:445
期:2
页码:1291-1299
全文大小:306 K
文摘
Let P be an m-homogeneous polynomial in n -complex variables x1,…,xn. Clearly, P has a unique representation in the form
and the m-form
satisfies e154179b08c98b0b41709c92" title="Click to view the MathML source">LP(x,…,x)=P(x) for every x∈Cn. We show that, although LP in general is non-symmetric, for a large class of reasonable norms on Cn the norm of LP on up to a logarithmic term (clogn)m2 can be estimated by the norm of P on ; here 30e6572fc7b46b1f8431e45a204f058" title="Click to view the MathML source">c≥1 denotes a universal constant. Moreover, for the ℓp-norms , 1≤p<2 the logarithmic term in the number n of variables is even superfluous.