Fourier integrals and sobolev imbedding on rearrangement invariant quasi-banach function spaces

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21 Citations (Scopus)

Abstract

We extend the mapping properties for the fractional integral operators, the convolution operators, the Fourier integral operators and the oscillatory integral operators to rearrangement-invariant quasi-Banach function spaces. We also generalize the Fourier restriction theorem and the Sobolev embedding theorem to rearrangement-invariant quasi-Banach function spaces. We obtain the above results by introducing two families of rearrangement-invariant quasi-Banach function spaces. Furthermore, these two families of rearrangement-invariant quasi-Banach function spaces also give us some embedding and interpolation results of Triebel-Lizorkin type spaces and Hardy type spaces built on rearrangement-invariant quasi-Banach function spaces. © 2016, Annales Academiæ Scientiarum Fennicæ Mathematica.
Original languageEnglish
Pages (from-to)897-922
JournalAnnales Academiæ Scientiarum Fennicæ Mathematica
Volume41
DOIs
Publication statusPublished - 2016

Citation

Ho, K.-P. (2016). Fourier integrals and sobolev imbedding on rearrangement invariant quasi-banach function spaces. Annales Academiæ Scientiarum Fennicæ Mathematica, 41, 897-922. doi: 10.5186/aasfm.2016.4157

Keywords

  • Fourier integral operator
  • Sobolev embedding
  • Oscillatory integrals
  • Hausdorff-Young inequalities
  • Restriction theorem
  • Rearrangement-invariant
  • Quasi-Banach function spaces
  • interpolation of operators
  • Triebel-Lizorkin spaces
  • Hardy spaces

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