Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions

Details Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions

2010-02-17

arxiv.org/abs/1002.3319v3

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jat.2011.10.004

For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{d}{dx}f+x^2 f. We define an atomic Hardy space H^1_{at}(X), which is a subspace of L^1((0,infty), x^alpha dx). Then we prove that the space H^1_{at}(X) is also characterized by the Riesz transform Rf=\sqrt{\pi}\frac{d}{dx}L^{-1/2}f in the sense that f\in H^1_{at}(X) if and only if f,Rf \in L^1((0,infty),x^alpha dx).

Affiliated with

Also associated with

No associations

Rating

Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-52241