{
  "id": "0804.1730",
  "version": "v3",
  "published": "2008-04-10T15:18:04.000Z",
  "updated": "2009-11-25T14:32:29.000Z",
  "title": "Micro-local analysis in Fourier Lebesgue and modulation spaces. Part I",
  "authors": [
    "Stevan Pilipovic",
    "Nenad Teofanov",
    "Joachim Toft"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "Let $\\omega ,\\omega_0$ be appropriate weight functions and $q\\in [1,\\infty ]$. We introduce the wave-front set, $\\WF_{\\mathscr FL^q_{(\\omega)}}(f)$ of $f\\in \\mathscr S'$ with respect to weighted Fourier Lebesgue space $\\mathscr FL^q_{(\\omega)}$. We prove that usual mapping properties for pseudo-differential operators $\\op (a)$ with symbols $a$ in $S^{(\\omega _0)}_{\\rho, 0}$ hold for such wave-front sets. Especially we prove \\WF_{\\mathscr FL^q_{(\\omega /\\omega_0)}}(\\op (a)f)\\subseteq \\WF_{\\mathscr FL^q_{(\\omega)}}(f) \\subseteq \\WF_{\\mathscr FL^q_{(\\omega /\\omega_0)}}(\\op (a)f)\\ttbigcup \\Char (a). %% Here $\\Char (a)$ is the set of characteristic points of $a$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-25T14:32:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A18",
      "35Sxx",
      "42B35",
      "47G30"
    ],
    "keywords": [
      "modulation spaces",
      "micro-local analysis",
      "wave-front set",
      "weighted fourier lebesgue space",
      "appropriate weight functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.1730P"
    }
  }
}