Optimizers for the finite-rank fractional Lieb--Thirring inequality

The finite-rank fractional Lieb--Thirring inequality provides an estimate on the Riesz sum of the first $N$ negative eigenvalues of the fractional Schrödinger operator $(-Δ)^s-V$ in terms of the $L^{γ+\frac{d}{2s}}(\mathbb R^d)$ norm of the potential $V$, where the Riesz exponent $γ>\max\left\{0,1-d