On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators

Details On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators

2010-06-27

arxiv.org/abs/1006.5189v1

Potential Anal. 35 (2011), no. 1, 39-50

Mathematics

Functional Analysis

Scientific paper

10.1007/s11118-010-9202-0

Let Lf(x)=-\Delta f(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a non-negative self-adjoint Schr\"odinger operator on R^d. We say that an L^1-function f belongs to the Hardy space H^1_L if the maximal function M_L f(x)=\sup_{t>0} |e^{-tL} f(x)| belongs to L^1(R^d). We prove that under certain assumptions on V the space H^1_L is also characterized by the Riesz transforms R_j=\frac{\partial}{\partial x_j} L^{-1/2}, j=1,...,d, associated with L. As an example of such a potential V one can take any V\geq 0, V\in L^1_{loc}, in one dimension.

Affiliated with

Also associated with

No associations

Rating

On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators 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 On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Riesz transforms characterization of H^1 spaces associated with some Schrödinger operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-630390