| Autor: |
Békollé, D., Bonami, A., Garrigós, G., Ricci, F., Sehba, B. |
| Rok vydání: |
2009 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We give various equivalent formulations to the (partially) open problem about $L^p$-boundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, $A^{p'}=(A^p)^*$, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequalities play an important role. For $p\geq 2$ we identify as a Besov space the range of the Bergman projection acting on $L^p$, and also the dual of $A^{p'}$. For the Bloch space $\SB^\infty$ we give in addition new necessary conditions on the number of derivatives required in its definition. |
| Databáze: |
arXiv |
| Externí odkaz: |
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