Fock-Sobolev Spaces of Fractional Order

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Abstract

For the full range of index (Formula presented.), real weight α and real Sobolev order s, two types of weighted Fock-Sobolev spaces over (Formula presented.), (Formula presented.) and (Formula presented.), are introduced through fractional differentiation and through fractional integration, respectively. We show that they are the same with equivalent norms and, furthermore, that they are identified with the weighted Fock space (Formula presented.) for the full range of parameters. So, the study on the weighted Fock-Sobolev spaces is reduced to that on the weighted Fock spaces. We describe explicitly the reproducing kernels for the weighted Fock spaces and then establish the boundedness of integral operators induced by the reproducing kernels. We also identify dual spaces, obtain complex interpolation result and characterize Carleson measures.

Original languageEnglish
Pages (from-to)199-240
Number of pages42
JournalPotential Analysis
Volume43
Issue number2
DOIs
Publication statusPublished - 2015 Aug 30

Keywords

  • Banach dual
  • Carleson measure
  • Complex interpolation
  • Fock-Sobolev space of fractional order
  • Weighted Fock space

ASJC Scopus subject areas

  • Analysis

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