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Classical harmonic analysis says that the spaces of homogeneous harmonicpolynomials (solutions of Laplace equation) are irreducible modules of thecorresponding orthogonal Lie group (algebra) and the whole polynomial algebrais a free module over the invariant polynomials generated by harmonicpolynomials. In this paper, we first establish two-parameter $\mbb{Z}^2$-gradedsupersymmetric oscillator generalizations of the above theorem for the Liesuperalgebra $gl(n|m)$. Then we extend the result to two-parameter$\mbb{Z}$-graded supersymmetric oscillator generalizations of the above theoremfor the Lie superalgebras $osp(2n|2m)$ and $osp(2n+1|2m)$.

Supersymmetyric Analogues of the Classical Theorem on Harmonic Polynomials