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Constructive Approximation

, Volume 27, Issue 3, pp 269–287 | Cite as

Hardy Spaces for Laguerre Expansions

  • Jacek DziubanskiEmail author
Article

Abstract

Let \({\cal L}_n^a(x)\) be the standard Laguerre functions of type a. We denote \(\varphi_n^a(x)={\cal L}_n^a(x^2)(2x)^{1\slash 2}\). Let \({\cal T}_tf(x)=\sum_{n}e^{-(n+(a+1)\slash 2)t} \langle f,{\cal L}_n^a\rangle {\cal L}_n^a(x)\) and \(T_tf(x)=\sum_{n}e^{-(4n+2a+2)t} \langle f,\varphi_n^a\rangle \varphi_n^a(x)\) be the semigroups associated with the orthonormal systems \({\cal L}^a_n\) and \(\varphi_n^a\). We say that a function f belongs to the Hardy space \(H^1\) associated with one of the semigroups if the corresponding maximal function belongs to \(L^1((0,\infty), dx)\). We prove special atomic decompositions of the elements of the Hardy spaces.

Keywords

Hardy Space Maximal Function Integral Kernel Weak Type Orthonormal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Institute of Mathematics, University of Wroclaw50-384 Wroclaw, pl. Grunwaldzki 2/4Poland

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