This paper is devoted to the study of weak Harnack inequalities for minimizers of nonlocal double phase functionals, whose prototype is given by \( \iint _{\mathbb {R}^n\times \mathbb {R}^n} \left( \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}+a(x,y)\frac{|u(x)-u(y)|^q}{|x-y|^{n+tq}}\right) \,dx\,dy, \) with \(a\ge 0\) and \(0<s,t<1<p\le q<\infty \) . The core of our approach is based on expansion of positivity and several measure theoretic estimates stemming from a nonlocal Caccioppoli-type inequality. The main challenge lies in controlling the subtle interaction between the pointwise behaviour of the modulating coefficient \(a(\cdot ,\cdot )\) and the structural exponents. In addition, we discuss a quantitative boundedness result for minimizers of such functionals.
