Abstract
In this article, two types of Hardy’s inequalities for the twisted convolution with Laguerre functions are studied. The proofs are mainly based on an estimate for the Heisenberg left-invariant vectors of the special Hermite functions deduced by the Heisenberg group approach.
Highlights
The classical Hardy’s inequalities on C state that if f (z) = ∞ k=ak zk belongs to the ordinaryHardy space Hp(C), < p ≤, one has the following results for the coefficients:|ak| ≤ ck /p– f Hp and ∞(k + )p– |ak|p ≤ cp f p H p, k=where cp depends only on p
The proofs of these inequalities are based on the atomic characterization of Hardy spaces
Hap(Cn) is the atomic Hardy space defined in terms of an atomic decomposition
Summary
The proofs of these inequalities are based on the atomic characterization of Hardy spaces. In this paper we continue to study Hardy’s inequalities for the twisted convolution with Laguerre functions defined by φk(z) = Lnk– In [ ], Radha and Thangavelu gave the following theorem, but the proof is left to the interested reader.
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