Besov and hardy spaces associated with the schrödinger operator on the heisenberg group

Ruming Gong; Ji Li; Liang Song

doi:10.1007/s12220-012-9331-3

Besov and hardy spaces associated with the schrödinger operator on the heisenberg group

Ruming Gong, Ji Li^*, Liang Song

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We introduce the Besov space Ḃ^0,L _1,1 associated with the Schrödinger operator L with a nonnegative potential satisfying a reverse Hölder inequality on the Heisenberg group, and obtain the molecular decomposition. We also develop the Hardy space H_L ¹ associated with the Schrödinger operator via the Littlewood-Paley area function and give equivalent characterizations via atoms, molecules, and the maximal function. Moreover, using the molecular decomposition, we prove that Ḃ^0,L _1,1 is a subspace of H_L ¹

Original language	English
Pages (from-to)	144-168
Number of pages	25
Journal	Journal of Geometric Analysis
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s12220-012-9331-3
Publication status	Published - Jan 2014
Externally published	Yes

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title = "Besov and hardy spaces associated with the schr{\"o}dinger operator on the heisenberg group",

abstract = "We introduce the Besov space Ḃ0,L 1,1 associated with the Schr{\"o}dinger operator L with a nonnegative potential satisfying a reverse H{\"o}lder inequality on the Heisenberg group, and obtain the molecular decomposition. We also develop the Hardy space HL 1 associated with the Schr{\"o}dinger operator via the Littlewood-Paley area function and give equivalent characterizations via atoms, molecules, and the maximal function. Moreover, using the molecular decomposition, we prove that Ḃ0,L 1,1 is a subspace of HL 1",

author = "Ruming Gong and Ji Li and Liang Song",

year = "2014",

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doi = "10.1007/s12220-012-9331-3",

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AU - Gong, Ruming

AU - Li, Ji

AU - Song, Liang

PY - 2014/1

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N2 - We introduce the Besov space Ḃ0,L 1,1 associated with the Schrödinger operator L with a nonnegative potential satisfying a reverse Hölder inequality on the Heisenberg group, and obtain the molecular decomposition. We also develop the Hardy space HL 1 associated with the Schrödinger operator via the Littlewood-Paley area function and give equivalent characterizations via atoms, molecules, and the maximal function. Moreover, using the molecular decomposition, we prove that Ḃ0,L 1,1 is a subspace of HL 1

AB - We introduce the Besov space Ḃ0,L 1,1 associated with the Schrödinger operator L with a nonnegative potential satisfying a reverse Hölder inequality on the Heisenberg group, and obtain the molecular decomposition. We also develop the Hardy space HL 1 associated with the Schrödinger operator via the Littlewood-Paley area function and give equivalent characterizations via atoms, molecules, and the maximal function. Moreover, using the molecular decomposition, we prove that Ḃ0,L 1,1 is a subspace of HL 1

UR - https://www.scopus.com/pages/publications/84891555581

U2 - 10.1007/s12220-012-9331-3

DO - 10.1007/s12220-012-9331-3

M3 - Article

AN - SCOPUS:84891555581

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SP - 144

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -

Besov and hardy spaces associated with the schrödinger operator on the heisenberg group

Abstract

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