Potential Analysis

, Volume 44, Issue 1, pp 109–136 | Cite as

Sharp Estimates for Potential Operators Associated with Laguerre and Dunkl-Laguerre Expansions

Open Access
Article

Abstract

We study potential operators associated with Laguerre function expansions of convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove qualitatively sharp estimates of the corresponding potential kernels. Then we characterize those 1 ≤ p,q8, for which the potential operators are Lp - Lq bounded. These results are sharp analogues of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and Dunkl-Laguerre settings.

Keywords

Laguerre Expansion Dunkl-Laguerre Expansion Laguerre Operator Dunkl Harmonic Oscillator Negative Power Potential Operator Fractional Integral Potential Kernel 

Mathematics Subject Classification (2010)

Primary 42C10 47G40 Secondary 31C15 26A33 

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Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Instytut MatematycznyPolska Akademia NaukWarszawaPoland
  2. 2.Wydział MatematykiPolitechnika WrocławskaWrocławPoland

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