Calderón–Zygmund Type Results for a Class of Quasilinear Elliptic Equations Involving the p(x)-Laplacian: Calderón–Zygmund Type Results for a Class

In this study, we obtain global Calderón–Zygmund-type estimates for weak solutions to quasilinear elliptic equations driven by p ( x )-Laplacian operator. We prove two results concerning both classical and generalized Lorentz spaces with two weights. Moreover, our interest in this paper is to estimate regularity estimates via fractional maximal operators and this tool is reminiscent of the idea described by Tran and Nguyen in (J. Funct. Anal. 280, 108797, 2021), (J. Differ. Equ. 268, 1427–1462, 2020), (J. Math. Anal. Appl. 509, 125928, 2022).