Sharp Estimates for Potential Operators Associated with Laguerre and Dunkl-Laguerre Expansions
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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 Lp - Lq bounded. These results are sharp analogues of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and Dunkl-Laguerre settings.
KeywordsLaguerre 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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