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We prove some weighted refined decoupling estimates. As an application, wegive an alternative proof of the following result on Falconer's distance setproblem by the authors in a companion work: if a compact set $E\subset\mathbb{R}^d$ has Hausdorff dimension larger than$\frac{d}{2}+\frac{1}{4}-\frac{1}{8d+4}$, where $d\geq 4$, then there is apoint $x\in E$ such that the pinned distance set $\Delta_x(E)$ has positiveLebesgue measure. Aside from this application, the weighted refined decouplingestimates may be of independent interest.

Weighted refined decoupling estimates and application to Falconer distance set problem