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,q ≤ 8, for which the potential operators are L p - L q bounded. These results are sharp analogues of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and Dunkl-Laguerre settings.
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This research was supported by the National Science Centre of Poland, project no. 2013/09/B/ST1/02057.
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Nowak, A., Stempak, K. Sharp Estimates for Potential Operators Associated with Laguerre and Dunkl-Laguerre Expansions. Potential Anal 44, 109–136 (2016). https://doi.org/10.1007/s11118-015-9501-6
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DOI: https://doi.org/10.1007/s11118-015-9501-6
Keywords
- Laguerre Expansion
- Dunkl-Laguerre Expansion
- Laguerre Operator
- Dunkl Harmonic Oscillator
- Negative Power
- Potential Operator
- Fractional Integral
- Potential Kernel