The Serrin exponent for Lane-Emden inequalities driven by sums of fractional p-Laplacians

We study positive weak super-solutions of the Lane-Emden inequality $\mathcal{L}u := \sum_{i=1}^{n}(-Δ_{p_i})^{s_i}u \ge u^q$ in $\mathbb{R}^N$, where each $(-Δ_{p_i})^{s_i}$ is a fractional $p_i$-Laplacian of order $s_i\in(0,1]$ and exponent $p_i\in(1,\infty)$, and $\max_i s_ip_i<N$. Let $κ_i := (N