Radial symmetry and sharp asymptotic behaviors of nonnegative solutions toweighted doubly \bm{<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="TIMEQ1"><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>}-critical quasi-linear nonlocal elliptic equations with Hardy potential

In this paper, we mainly consider nonnegative weak solutions $u\in~D^{1,p}(\R^{N})$ to the doubly $D^{1,p}(\R^{N})$-critical nonlocal quasi-linear Schrödinger-Hartree equation:beginalign*-Δp u- μ fracu^p-1x^p