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Volume 40, Issue 2
Carleson Measure Associated with the Fractional Heat Semigroup of Schrödinger Operator

Jizheng Huang & Shuangshuang Ying

Commun. Math. Res., 40 (2024), pp. 191-213.

Published online: 2024-05

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  • Abstract

Let $L=−∆+V$ be a Schrödinger operator, where $∆$ is the Laplacian on $\mathbb{R}^d$ and the nonnegative potential $V$ belongs to the reverse Hölder class $B_{d/2}.$ In this paper, we define a new version of Carleson measure associated with the fractional heat semigroup of Schrödinger operator $L.$ We will characterize the Campanato spaces and the predual spaces of the Hardy spaces by the new Carleson measure.

  • AMS Subject Headings

35J10, 42B25, 42B30

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COPYRIGHT: © Global Science Press

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@Article{CMR-40-191, author = {Huang , Jizheng and Ying , Shuangshuang}, title = {Carleson Measure Associated with the Fractional Heat Semigroup of Schrödinger Operator}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {2}, pages = {191--213}, abstract = {

Let $L=−∆+V$ be a Schrödinger operator, where $∆$ is the Laplacian on $\mathbb{R}^d$ and the nonnegative potential $V$ belongs to the reverse Hölder class $B_{d/2}.$ In this paper, we define a new version of Carleson measure associated with the fractional heat semigroup of Schrödinger operator $L.$ We will characterize the Campanato spaces and the predual spaces of the Hardy spaces by the new Carleson measure.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2024-0001}, url = {http://global-sci.org/intro/article_detail/cmr/23087.html} }
TY - JOUR T1 - Carleson Measure Associated with the Fractional Heat Semigroup of Schrödinger Operator AU - Huang , Jizheng AU - Ying , Shuangshuang JO - Communications in Mathematical Research VL - 2 SP - 191 EP - 213 PY - 2024 DA - 2024/05 SN - 40 DO - http://doi.org/10.4208/cmr.2024-0001 UR - https://global-sci.org/intro/article_detail/cmr/23087.html KW - Schrödinger operator, reverse Hölder class, Carleson measure, fractional heat semigroup, Campanato spaces. AB -

Let $L=−∆+V$ be a Schrödinger operator, where $∆$ is the Laplacian on $\mathbb{R}^d$ and the nonnegative potential $V$ belongs to the reverse Hölder class $B_{d/2}.$ In this paper, we define a new version of Carleson measure associated with the fractional heat semigroup of Schrödinger operator $L.$ We will characterize the Campanato spaces and the predual spaces of the Hardy spaces by the new Carleson measure.

Jizheng Huang & Shuangshuang Ying. (2024). Carleson Measure Associated with the Fractional Heat Semigroup of Schrödinger Operator. Communications in Mathematical Research . 40 (2). 191-213. doi:10.4208/cmr.2024-0001
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