Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications

Let $λ>-1/2,\neq0$. Consider the Bessel operators \begin{align*} Δ_λ:=-\frac{d^2}{dx^2}-\frac{2λ}{x}\frac{d}{dx} \end{align*} on $\mathbb{R}_+$. In this paper, we first establish several characterizations for $\widetilde{A}_{\infty,λ}$ weights introduced by Li et al. (Math. Z. 309(1) (2025), Paper N