The König constant is one

Xinyuan Xie, Haonan Zhang

For each $N\ge 1$, consider the normalized König bilinear form $B_{\mathrm{K}}:L_{\infty }({\mathbb{R}}^N)\times L_{\infty }({\mathbb{R}}^N)\to \mathbb{R}$ given by \[ B_{\mathrm K}(f,g):=\frac{1…