JournalszaaVol. 23 , No. 4DOI 10.4171/zaa/1219

On Representation, Boundedness and Convergence of Hankel-K{Mp}' Generalized Functions

  • Isabel Marrero

    Universidad de La Laguna, Spain
On Representation, Boundedness and Convergence of Hankel-K{Mp}' Generalized Functions cover

Abstract

Under opportune assumptions on the defining sequence {Mp}p=0\{M_p\}_{p=0}^{\infty}, Hankel-K{Mp}K\{M_{p}\}' generalized functions can be represented as

f=xμ12(Dx1)kF(x),f = x^{-\mu-\frac{1}{2}}(Dx^{-1})^kF(x),

where kNk\in {\mathbb N} and FF is a continuous function on I=(0,)I=(0,\infty) such that Mr1FLq(I)M^{-1}_r F\in L^q(I) (1q)(1\le q\le \infty) for some rNr\in {\mathbb N}. A corresponding characterization of boundedness and convergence of Hankel-K{Mp}K\{M_{p}\}' generalized functions is given.