A REGULARITY THEORY FOR PARABOLIC EQUATIONS WITH ANISOTROPIC NONLOCAL OPERATORS IN SPACES

In this paper, we present an Lq(Lp)-regularity theory for parabolic equations of the operators encompassing the singular anisotropic fractional Laplacian with measurable coefficients: i=1 | yi| 1+\alpha i dyi. To address the anisotropy of the operator, we employ a probabilistic representation of the solution and Calder\'on-Zygmund theory. As applications of our results, we demonstrate the solvability of elliptic equations with anisotropic nonlocal operators and parabolic equations with isotropic nonlocal operators.