AN EXTENSION OF A NORM INEQUALITY FOR A SEMI-DISCRETE gλ* FUNCTION

A norm inequality for a semi-discrete $g_{lambda}^{ast }(f)$ function is obtained for functions, $f$, that can be written as a sum whose terms consist of a numerical coefficient multiplying a member of a family of functions that have properties of geometric decay, minimal smoothness and almost orthogonality condition. The theorem is applied to the rate of change of $u$, a solution to $Lu=diveoverrightarrow{f}$ in a bounded, nonsmooth domain $Omega subset mathbb{R}^{d}$, $dgeq 3$, $u=0$ on $partial Omega $.