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 82934c16a217cb876931f2ad3c9d" title="Click to view the MathML source">x1,…,xn. Clearly, P has a unique representation in the form
satisfies 98b0b41709c92" title="Click to view the MathML source">LP(x,…,x)=P(x) for every x∈Cn. We show that, although 82b5107f09ff783edacefc" title="Click to view the MathML source">LP in general is non-symmetric, for a large class of reasonable norms 83f071dafac35731"> on e858350f8184d8533ad8f9dd1" title="Click to view the MathML source">Cn the norm of 82b5107f09ff783edacefc" title="Click to view the MathML source">LP on up to a logarithmic term 9c3576ac3897fd6e65ce7" title="Click to view the MathML source">(clogn)m2 can be estimated by the norm of P on 94c7cebb58fe9ae6d866fabaf63e5b2">; here c≥1 denotes a universal constant. Moreover, for the ℓp-norms 8297f29ce4d865eeedf42">, e8527e3073507043352050fe22260" title="Click to view the MathML source">1≤p<2 the logarithmic term in the number n of variables is even superfluous.