= Monotonicity of uniform sparse recovery in the exponent
If the <Lq null space property> holds at $q\le1$, it holds at every $0<p<q$. Order a nonzero null <vector>'s magnitudes $a_1\ge\cdots\ge a_N$ and put $t=a_s>0$. Since $p-q<0$, the top-$s$ $p$-power sum is at most $t^{p-q}$ times its $q$-power sum, while the tail $p$-power sum is at least that multiple of the tail $q$-power sum. The strict $q$ inequality therefore gives the strict $p$ inequality. The largest $s$ magnitudes are the worst <support of a vector>, so all other supports satisfy it too.
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