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Suppose Q is a bounded, strongly convex domain in CN with smooth boundary and q: Q Q is an arbitrary holomorphic map. While in general the composition operator C?, need not map the Hardy space HP(Q) into itself when N > 1, our main theorem shows that C?, does map HP (Q) boundedly into a certain weighted Bergman space on Q, where the weight function depends on the dimension N. We also consider properties of C?, on HP(Q) when 0(Q) is contained in an approach region in Q.

Composition operators between Hardy and weighted Bergman spaces on convex domains in 𝐶^{𝑁}