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Poletsky-Stessin Hardy spaces, dened in [2], are the natural generalizations of Hardy spaces on hyperconvex domains and the Cauchy-Fantappie projections are the $n$- dimensional analogs of Cauchy integral of the one variable theory. In the rst part of this talk we will consider the boundedness and compactness properties of Cauchy-Fantappietype projections on Poletsky-Stessin Hardy spaces $H^p_u(B^p)$ of complex ellipsoids. We show that the boundedness and compactness of these operators can be characterized through the conditions known as Carleson conditions. This characterization enables us to relate the PSHardy spaces generated by an arbitrary exhaustion function $\phi$ to the $H^p_u(B^p)$ for which we have a better understanding. In the second part of the talk, we will mention Grothendieck- Kothe-da Silva duality for the spaces of holomorphic functions dened in a convex domain and then using a general characterization of dual complements of Reinhardt domains by [1], we give the dual complement of some special type of complex ellipsoids. Moreover, we present a duality result for Poletsky-Stessin Hardy space of complex ellipsoid analogous to that of [1] on classical Hardy spaces.