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Session 18. Harmonic analysis, orthogonal expansions and Dunkl theory
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Potential operators associated with Hankel-Dunkl and Laguerre-Dunkl expansions |
Adam Nowak, Institute of Mathematics, Polish Academy of Sciences, Poland
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The talk is based on the joint work with Krzysztof Stempak
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We study analogues of Riesz and Bessel potentials in the frameworks related to the Dunkl Laplacian
and the Dunkl harmonic oscillator, where the underlying group of reflections is
isomorphic to \(\boldsymbol{Z}_2^d\).
We discuss sharp or qualitatively sharp pointwise estimates of the associated potential kernels.
We also describe those \(1 \le p,q \le \infty\), for which the potential operators are \(L^p-L^q\) bounded.
The latter results are counterparts of the classical Hardy-Littlewood-Sobolev fractional integration
theorem in the above mentioned settings.
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References- A.Nowak, K.Stempak,
Sharp estimates for potential operators associated with Laguerre and Dunkl-Laguerre expansions ,
preprint 2013. arXiv:1402.2522
- A.Nowak, K.Stempak,
Potential operators associated with Hankel and Hankel-Dunkl transforms ,
preprint 2014. arXiv:1402.3399
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