Characterizations of a class of Pilipovi 'c spaces by powers of\n harmonic oscillator

2019/05/26 by Ahmed Abdeljawad, Abdeljawad, Ahmed, Carmen Fernández +7
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1905.10732

openalex publication_date 2019/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a smooth function f on mathbf R^d belongs to the\nPilipovi 'c space mathcal H _{flat _\σ}( mathbf R^d) or the\nPilipovi 'c space mathcal H_{0, flat _\σ}( mathbf R^d), if and only if\nthe L^p norm of H_d^Nf for N\≥ 0, satisfy certain types of estimates.\nHere H_d=|x|²-\Δ _x is the harmonic oscillator.\n

Related

• Fourier characterizations of Pilipovic spaces
• The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces
• Lipschitz spaces and bounded mean oscillation of harmonic mappings
• Harmonic spaces
• Properties for (α,β)-harmonic functions