Gradient higher integrability of bounded solutions to parabolic double-phase systems

We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon $$u_t-\text{dv}(\mathrm{\mid }\text{na}u{\mathrm{\mid }}^{p-2}\text{na}u+a(x,t)\mathrm{\mid }\text{na}u{\mathrm{\mid }}^{q-2}\text{na}u)=-\text{dv}(\mathrm{\mid }F{\mathrm{\mid }}^{p-2}F+a(x,t)\mathrm{\mid }F{\mathrm{\mid }}^{q-2}F),$$ where a nonnegative weight $a$ is $\alpha$-Hölder continuous in space and $\frac{\alpha }{2}$-Hölder continuous in time, have locally higher integrable gradients for the sharp range of exponents $p<q\le p+\alpha$.