Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $NA$ groups

Utsav Dewan

Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $NA$ groups

Classical Analysis and ODEs 2022-06-17 v1 Analysis of PDEs

Authors: Utsav Dewan

Abstract

We prove a converse of Fatou type result for certain eigenfunctions of the Lalplace-Beltrami operator on Harmonic NA groups relating sectorial convergence and admissible convergence of Poisson type integrals of complex (signed) measures. This result extends several results of this kind proved eariler in the context of the classical upper half space $\mathbb{R}_+^{n+1}$ . Similar results are also obtained in the degenerate case of the real hyperbolic spaces.

Keywords

harmonic na groups poisson integrals admissible convergence sectorial convergence fatou theorem laplace-beltrami operator real hyperbolic spaces

Cite

@article{arxiv.2206.08142,
  title  = {Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $NA$ groups},
  author = {Utsav Dewan},
  journal= {arXiv preprint arXiv:2206.08142},
  year   = {2022}
}

Comments

22 pages. arXiv admin note: text overlap with arXiv:2105.04964 by other authors

Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $NA$ groups

Abstract

Keywords

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