Abstract
We obtain a generalization of Hardy’s inequality for functions in the Hardy space H1 (Bd), where Bd is the unit ball {z = (z1, …, zd) ∈ In particular, we construct a function φ on the set of d –dimensional multi-indices {n = (n1, …, nd) | ni ∈ {0}} and prove that if f(z) = Σ anzn is a function in H1 (Bd), then ≤ Moreover, our proof shows that this inequality is also valid for functions in Hardy space on the polydisk H1 (Bd).
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