Guan-Cheng Pan

Mockenhaupt's Three-Term Hardy-Littlewood Majorant Conjecture

For an integer $k \ge 0$, let $f_k(x) = 1 + e(x) + e((k+2)x)$ and $g_k(x) = 1 + e(x) - e((k+2)x)$ on $\mathbb{T} = \mathbb{R}/\mathbb{Z}$, where $e(x) = e^{2\pi i x}$. Mockenhaupt conjectured that $\|g_k\|_{L^p(\mathbb{T})}>\|f_k\|_{L^p(\mathbb{T})}$ whenever $2k<p<2k+2$. The conjecture was previously known for $k \le...