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.
Publié le : 2000-05-14
Classification:
Fractional integration,
Laguerre and Hermite expansions,
Hankel transforms,
multipliers,
26A33,
26D15,
33C45,
42C10
@article{1178224609,
author = {Gasper, George and Trebels, Walter},
title = {Norm inequalities for fractional integrals of Laguerre and Hermite expansions},
journal = {Tohoku Math. J. (2)},
volume = {52},
number = {4},
year = {2000},
pages = { 251-260},
language = {en},
url = {http://dml.mathdoc.fr/item/1178224609}
}
Gasper, George; Trebels, Walter. Norm inequalities for fractional integrals of Laguerre and Hermite expansions. Tohoku Math. J. (2), Tome 52 (2000) no. 4, pp. 251-260. http://gdmltest.u-ga.fr/item/1178224609/