发表机构
Oklahoma State University（俄克拉荷马州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明复多项式Hardy--Littlewood常数在$p\geq c m^2/\log m$时呈多项式增长，推广了Bohnenblust--Hille常数的结果，并给出实情形下的渐近界。
AI 中文摘要
我们证明了复多项式Hardy--Littlewood不等式中的最优常数在$p\geq c m^2/\log m$（对每个固定$c>0$）时具有多项式增长界。这将在$p=\infty$处最近建立的复多项式Bohnenblust--Hille常数的多项式增长推广到有限的$p$值。此外，当$p/m^2\to\infty$时，Hardy--Littlewood常数被$(1+o(1))$倍的相应Bohnenblust--Hille常数所界定。对于实标量，当$p_m/m\to\infty$时，最优常数满足$H^{\rm pol}_{m,p_m}(\mathbb R)=2^{m+o(m)}$。
英文摘要
The polynomial Hardy--Littlewood inequalities bound coefficient norms of homogeneous polynomials on $\ell_p$ balls by their supremum norms, with constants independent of the dimension. Their $p=\infty$ endpoint is the Bohnenblust--Hille inequality. A longstanding obstruction to connecting their constants is the polarization loss in the usual multilinear approach. We overcome this obstruction by proving $D_{m,p_m}\le(1+o(1))D_m$ whenever $p_m/m^2\to\infty$, where $D_{m,p}$ and $D_m$ are the optimal complex polynomial Hardy--Littlewood and Bohnenblust--Hille constants. At the opposite boundary, we determine the optimal endpoint constant exactly, $D_{m,m}=m$. We then prove the full first-order asymptotic $D_{m,p_m}\sim m$ whenever $p_m\ge m$ and $p_m-m\to0$, and the exact polynomial growth $D_{m,p_m}=m^{1+o(1)}$ on the wider scale $p_m-m=o((m/\log m)^{1/3})$.
Comments43 pages. The paper has been refocused on the complex setting, and the exposition has been revised throughout. No substantial changes to the main results
