Local Hessian estimate for second order parabolic equation in Hardy spaces - Trung, Nguyen Duc; Truong, Le Xuan; Do, Tan Duc; Trong, Nguyen Ngoc (Mathematica Scandinavica, 2025)
We derive an interior estimate up to second orders in Hardy spaces for solutions to the parabolic problem cases u_t - _i, j=1^n a_i j ^2_ij u = f & in Ω _T, u h^p(0,T; h^1,p(Ω )) h^1,p_loc (0,T ; h^2,p_loc (Ω )) cases within an appropriate framework. In the course of proof, we also establish the boundedness results of parabolic singular integrals and their commutators on Hardy spaces which are of independent interest.