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Regularity of fractional heat semigroups associated with Schrödinger operators on Heisenberg groups

  • Chuanhong Sun , Pengtao Li ORCID logo EMAIL logo and Zengjian Lou EMAIL logo
Published/Copyright: January 2, 2024
Forum Mathematicum
From the journal Forum Mathematicum Volume 36 Issue 6

Abstract

Let L = - Δ ℍ n + V be a Schrödinger operator on Heisenberg groups ℍ n , where Δ ℍ n is the sub-Laplacian, the nonnegative potential V belongs to the reverse Hölder class B 𝒬 / 2 . Here 𝒬 is the homogeneous dimension of ℍ n . In this article, we introduce the fractional heat semigroups { e - t ⁢ L α } t > 0 , α > 0 , associated with L. By the fundamental solution of the heat equation, we estimate the gradient and the time-fractional derivatives of the fractional heat kernel K α , t L ⁢ ( ⋅ , ⋅ ) , respectively. As an application, we characterize the space BMO L γ ⁢ ( ℍ n ) via { e - t ⁢ L α } t > 0 .

Keywords: Schrödinger operators; regularity properties; Heisenberg group; Reverse Hölder inequality
MSC 2020: 22E30; 42B35; 35J10; 47B38

Communicated by Christopher D. Sogge

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 12071272

Funding source: Natural Science Foundation of Shandong Province

Award Identifier / Grant number: ZR2020MA004

Funding statement: The research was supported by the National Natural Science Foundation of China (Grant No. 12071272) and Shandong Natural Science Foundation of China (Grant No. ZR2020MA004).

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Received: 2023-08-09
Published Online: 2024-01-02
Published in Print: 2024-09-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Regularity of fractional heat semigroups associated with Schrödinger operators on Heisenberg groups
  3. Generalized orthogonal measures on the space of unital completely positive maps
  4. Multiplicity of solutions for a singular system with sign-changing potential
  5. Enochs’ conjecture for cotorsion pairs and more
  6. A fixed point theorem for isometries on a metric space
  7. Topological embeddings into transformation monoids
  8. Two curious q-supercongruences and their extensions
  9. Wells-type exact sequence and crossed extensions of algebras with bracket
  10. What conjugate phase retrieval complex vectors can do in quaternion Euclidean spaces
  11. Hardy inequalities on metric measure spaces, IV: The case p=1
  12. Cellular covers of divisible uniserial modules over valuation domains
  13. Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order
  14. Algebraic results on rngs of singular functions
  15. Degrees of generalized Kloosterman sums
  16. Normalized solutions for the fractional Schrödinger equation with combined nonlinearities
  17. On 𝐿𝑝 boundedness of rough Fourier integral operators
https://doi.org/10.1515/forum-2023-0285
Keywords for this article
Schrödinger operators; regularity properties; Heisenberg group; Reverse Hölder inequality

Articles in the same Issue

  1. Frontmatter
  2. Regularity of fractional heat semigroups associated with Schrödinger operators on Heisenberg groups
  3. Generalized orthogonal measures on the space of unital completely positive maps
  4. Multiplicity of solutions for a singular system with sign-changing potential
  5. Enochs’ conjecture for cotorsion pairs and more
  6. A fixed point theorem for isometries on a metric space
  7. Topological embeddings into transformation monoids
  8. Two curious q-supercongruences and their extensions
  9. Wells-type exact sequence and crossed extensions of algebras with bracket
  10. What conjugate phase retrieval complex vectors can do in quaternion Euclidean spaces
  11. Hardy inequalities on metric measure spaces, IV: The case p=1
  12. Cellular covers of divisible uniserial modules over valuation domains
  13. Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order
  14. Algebraic results on rngs of singular functions
  15. Degrees of generalized Kloosterman sums
  16. Normalized solutions for the fractional Schrödinger equation with combined nonlinearities
  17. On 𝐿𝑝 boundedness of rough Fourier integral operators
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