The non-existence results for a class of integral equation

In this paper, we consider the following integral system(0.1)u(x,b)=∫Rnuq(y,b)(b+|x−y|)λdy, which is related to the weak type convolution-Youngʼs inequality. Under the assumption of that λ∈(0,n) and 02), which implies that the maximizing pair of the weak type convolution-Youngʼs inequality with kernel function (b+|x|)−λ does not exist. Meanwhile, for λ∈(−∞,0) and q=2n/λ−1, we also show that the system (0.1) doesnʼt admit non-negative Lebesgue measurable solution. This is distinct from the original conformal invariant integral system.