$q$-Heisenberg Algebra in ${\otimes }^2-$Tensor Space

In this paper, we introduce the $q$-Heisenberg algebra in the tensor product space ${\otimes }^2$. We establish its algebraic properties and provide applications to the theory of non-monogenic functions. Our results extend known constructions in $q$-deformed algebras and offer new insights into functional analysis in non-commutative settings.