Split functions, Fourier transforms and multipliers

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• 作者：Laura De Carli ; Steve Hudson
• 关键词：42B15 ; 42B10
• 刊名：Collectanea Mathematica
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：66
• 期：2
• 页码：297-309
• 全文大小：250 KB
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  7.De Carli, L., Laeng, E.: On the (p, p) norm of monotonic Fourier multipliers. C. R. Acad. Sci. Paris S茅r. I Math. 330(8), 657鈥?62 (2000)View Article MATH
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  13.Nazarov, F.L., Podkorytov, A.N.: On the behavior of the Lebesgue constants for two-dimensional Fourier sums over polygons. St. Petersburg Math. J. 7, 663鈥?80 (1996)MathSciNet
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  17.Verbitsky I.E.: An estimate of the norm of a function in a Hardy space in terms of the norms of its real and imaginary parts. AMS. Transl. (2):11鈥?5, (1984) (Translation of Mat. Issled. Vyp. 54 (1980) 16鈥?0)
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• 作者单位：Laura De Carli (1)
  Steve Hudson (1)
  
  1. FIU, Miami, FL, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Analysis
  Applications of Mathematics
  Geometry
  
• 出版者：Springer Milan
• ISSN：2038-4815

文摘

We study the \(L^p\) norm of the Fourier transform of \(S_t\!f\), where \(S_t\) is a splitting operator. If \(m\) is a Fourier multiplier, we also study the operator norm of \(S_t m\). Most of our results assume \(p\) is an even integer. They are often stronger when \(f\) or \(m\) has compact support.