L^∞ to L^p constants for Riesz projections

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• 作者：Jordi Marzo ; ^a ; ^{jordi.marzo@math.ntnu.no} ; Kristian Seip^a ; ^{kristian.seip@math.ntnu.no}
• 关键词：Riesz transform ; Best constants ; Critical exponents
• 刊名：Bulletin des Sciences Mathematiques
• 出版年：2011
• 出版时间：April-May 2011
• 年：2011
• 卷：135
• 期：3
• 页码：324-331
• 全文大小：114 K

文摘

The norm of the Riesz projection from to is considered. It is shown that for n=1, the norm equals 1 if and only if p4 and that the norm behaves asymptotically as p/(πe) when p→∞. The critical exponent p_n is the supremum of those p for which the norm equals 1. It is proved that 2+2/(2ⁿ−1)p_n<4 for n>1; it is unknown whether the critical exponent for n=∞ exceeds 2.