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 9d" title="Click to view the MathML source">x1,…,xn. Clearly, P has a unique representation in the form
satisfies LP(x,…,x)=P(x) for every x∈Cn. We show that, although b37682b5107f09ff783edacefc" title="Click to view the MathML source">LP in general is non-symmetric, for a large class of reasonable norms 83f071dafac35731"> on 8350f8184d8533ad8f9dd1" title="Click to view the MathML source">Cn the norm of b37682b5107f09ff783edacefc" title="Click to view the MathML source">LP on up to a logarithmic term e65ce7" title="Click to view the MathML source">(clogn)m2 can be estimated by the norm of P on b58fe9ae6d866fabaf63e5b2">; here e6572fc7b46b1f8431e45a204f058" title="Click to view the MathML source">c≥1 denotes a universal constant. Moreover, for the 863f7b1bfd6a9e351210a" title="Click to view the MathML source">ℓp-norms 865eeedf42">, 1≤p<2 the logarithmic term in the number n of variables is even superfluous.