Title: Representations of Super $W(2,2)$ algebra $\mathfrak{L}$,
Abstract: In paper, we study the representation theory of super $W(2,2)$ algebra
${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible
modules and give the classification of irreducible modules of intermediate
series. We determinate the conjugate-linear anti-involution of ${\mathfrak{L}}$
and give the unitary modules of intermediate series.