Some estimates for commutators of Riesz transform associated with Schrödinger type operators

Title:

Some estimates for commutators of Riesz transform associated with Schrödinger type operators

Creator:

Liu, Yu, Zhang, Jing, Sheng, Jie-Lai, and Wang, Li-Juan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:64ff85f3-0d82-40a5-964e-abc482234a46
uuid:64ff85f3-0d82-40a5-964e-abc482234a46
issn:0011-4642

Subject:

mathematics, Schrödinger equation, commutator, Hardy space, everse Hölder inequality, Riesz transform, Schrödinger operator, Schrödinger type operator, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let L1 = −Δ + V be a Schrödinger operator and let L2 = (−Δ)2 + V2 be a Schrödinger type operator on \mathbb{R}^{n}\left ( n\geqslant 5 \right ) where V≠ 0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s\geqslant n/2. The Hardy type space H_{L2}^{1} is defined in terms of the maximal function with respect to the semigroup \left\{ {{e^{ - t{L_2}}}} \right\} and it is identical to the Hardy space H_{L2}^{1} established by Dziubański and Zienkiewicz. In this article, we prove the Lp-boundedness of the commutator Rb = bRf - R(bf) generated by the Riesz transform R = {\nabla ^2}L_2^{ - 1/2} , where b \in BM{O_\theta }(\varrho ) , which is larger than the space BMO\left (\mathbb{R}^{n} \right ). Moreover, we prove that Rb is bounded from the Hardy space H_{L2}^{1} into weak L_{weak}^1 (\mathbb{R}^n )., Yu Liu, Jing Zhang, Jie-Lai Sheng, Li-Juan Wang., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

169-191

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:1

Harvested from:

CDK

Metadata only:

false