Some results on Gaussian Besov–Lipschitz spaces and Gaussian Triebel–Lizorkin spaces
| Autor: | Wilfredo Urbina, Ebner Pineda |
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| Rok vydání: | 2009 |
| Předmět: |
Mathematics::Functional Analysis
Mathematics(all) Numerical Analysis Hermite polynomials General Mathematics Gaussian Bessel potentials Applied Mathematics Mathematical analysis Fractional integrals Mathematics::Classical Analysis and ODEs Fractional derivatives Context (language use) Triebel–Lizorkin spaces Lipschitz continuity Hermite expansions Sobolev space symbols.namesake symbols Laguerre polynomials Besov–Lipschitz spaces Bessel function Analysis Mathematics Interpolation |
| Zdroj: | Journal of Approximation Theory. 161(2):529-564 |
| ISSN: | 0021-9045 |
| DOI: | 10.1016/j.jat.2008.11.010 |
| Popis: | In this paper we define Besov–Lipschitz and Triebel–Lizorkin spaces in the context of Gaussian harmonic analysis, the harmonic analysis of Hermite polynomial expansions. We study inclusion relations among them, some interpolation results and continuity results of some important operators (the Ornstein–Uhlenbeck and the Poisson–Hermite semigroups and the Bessel potentials) on them. We also prove that the Gaussian Sobolev spaces Lαp(γd) are contained in them. The proofs are general enough to allow extensions of these results to the case of Laguerre or Jacobi expansions and even further in the general framework of diffusion semigroups. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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