Hardy's inequality for functions of several complex variables
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 f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia,
2017-09.
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| Online Access: | Get fulltext |
| Summary: | 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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