The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation

The paper is concerned with the relationship between the nontangential maximal function of the solution to a Dirichlet problem with an -boundary function, , for a second-order elliptic equation and the Luzin area integral. The equation is considered in the self-adjoint form without lower-degree terms. The -norm of the nontangential maximal function of the solution is estimated from above and below in terms of the squared -norm of the area integral of . Here the coefficients of the equation need not be smooth in the domain. Bibliography: 33 titles.