Bergman spaces of temperature functions on a cylinder

Marcos López-García

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-21

Abstract:

We define the weighted Bergman space b β p ( S T ) consisting of temperature functions on the cylinder S T = S 1 × ( 0 , T ) and belonging to L p ( Ω T , t β d x d t ) , where Ω T = ( 0 , 2 ) × ( 0 , T ) . For β > − 1 we construct a family of bounded projections of L p ( Ω T , t β d x d t ) onto b β p ( S T ) . We use this to get, for 1 < p < ∞ and 1 / p + 1 / p ′ = 1 , a duality b β p ( S T ) ∗ = b β ′ p ′ ( S T ) , where β ′ depends on p and β .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:348261

DOI: 10.1155/S0161171203204178

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