On a restriction problem of de Leeuw type for Laguerre multipliers

  title={On a restriction problem of de Leeuw type for Laguerre multipliers},
  author={George Gasper and Walter Trebels},
  journal={Acta Mathematica Hungarica},
In 1965 K. de Leeuw [3] proved among other things in the Fourier transform setting: If a continuous function m(ξ1, . . . , ξn) on R generates a bounded transformation on L(R), 1 ≤ p ≤ ∞, then its trace m(ξ1, . . . , ξk) = m(ξ1, . . . , ξk, 0, . . . , 0), k < n, generates a bounded transformation on L(R). In this paper, the analogous problem is discussed in the setting of Laguerre expansions of different orders. 

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AbstractПолучены оценки свер ху и снизу для разложе ний по собственным функция м дифференциального уравнения Лагерра в е го нормальной лиувил левой форме в пространствеLp(0, ∞). Этот тип разложений о