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 $L_p$-boundary function, $p>1$, 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 $L_p$-norm of the nontangential maximal function of the solution $u$ is estimated from above and below in terms of the squared $L_2(\partial Q)$-norm of the area integral of $v=|u|^{p/2}$. Here the coefficients of the equation need not be smooth in the domain.
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