$L^p$ Boundedness of Commutators of Riesz Transforms associated to Schrödinger Operator

Mathematics – Classical Analysis and ODEs

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

14 pages, 0 figures

Scientific paper

In this paper we consider $L^p$ boundedness of some commutators of Riesz transforms associated to Schr\"{o}dinger operator $P=-\Delta+V(x)$ on $\mathbb{R}^n, n\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and belongs to $B_q$ for some $q \geq n/2$. Let $T_1=(-\Delta+V)^{-1}V,\ T_2=(-\Delta+V)^{-1/2}V^{1/2}$ and $T_3=(-\Delta+V)^{-1/2}\nabla$. We obtain that $[b,T_j] (j=1,2,3)$ are bounded operators on $L^p(\mathbb{R}^n)$ when $p$ ranges in a interval, where $b \in \mathbf{BMO}(\mathbb{R}^n)$. Note that the kernel of $T_j (j=1,2,3)$ has no smoothness.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

$L^p$ Boundedness of Commutators of Riesz Transforms associated to Schrödinger Operator 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 $L^p$ Boundedness of Commutators of Riesz Transforms associated to Schrödinger Operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $L^p$ Boundedness of Commutators of Riesz Transforms associated to Schrödinger Operator will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-579996

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.