Abstract
Suppose the fractional integration operator $I^{\sigma}$ is generated by the sequence $\{(k+1)^{-\sigma}\}$ in the setting of Laguerre and Hermite expansions. Then, via projection formulas, the problem of the norm boundedness of $I^{\sigma}$ is reduced to the well-known fractional integration on the half-line. A corresponding result with respect to the modified Hankel transform is derived and its connection with the Laguerre fractional integration is indicated.
Citation
George Gasper. Walter Trebels. "Norm inequalities for fractional integrals of Laguerre and Hermite expansions." Tohoku Math. J. (2) 52 (2) 251 - 260, 2000. https://doi.org/10.2748/tmj/1178224609
Information