Gradient estimates for singular elliptic measure data problems with double phase

We consider elliptic measure data problems of the type $$-\mathrm{d}\mathrm{i}\mathrm{v}(\mathrm{\mid }Du{\mathrm{\mid }}^{p-2}Du+a(x)\mathrm{\mid }Du{\mathrm{\mid }}^{q-2}Du)=\mu$$ in a bounded domain in ${\mathbb{R}}^n$, where $p<q$ and $a(\cdot )\ge 0$. We prove local Calderón–Zygmund estimates in the singular case $2-1\mathrm{/}n<p<2$, under natural assumptions on $p$, $q$ and $a(\cdot )$.