Fractional operators of variable order from variable exponent Morrey spaces to variable exponent Campanato spaces on quasi-metric measure spaces with growth condition

Humberto Rafeiro, Stefan Samko

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We study fractional potential of variable order on a bounded quasi-metric measure space (X,d,μ) as acting from variable exponent Morrey space Lp(·),λ(·)(X) to variable exponent Campanato space Lp(·),λ(·)(X). We assume that the measure satisfies the growth condition μB(x,r)⩽Crγ, the distance is θ-regular in the sense of Macías and Segovia, but do not assume that the space (X,d,μ) is homogeneous. We study the situation when γ-λ(x)⩽α(x)p(x)⩽γ-λ(x)+θp(x), and pay special attention to the cases of bounds of this interval. The left bound formally corresponds to the BMO target space. In the case of right bound a certain “correcting factor” of logarithmic type should be introduced in the target Campanato space.

Original languageEnglish
Pages (from-to)803-818
Number of pages16
JournalRicerche di Matematica
Volume73
Issue number2
DOIs
Publication statusPublished - Apr 2024

Keywords

  • 26A33
  • 46E30
  • Campanato space
  • Fractional operator
  • Morrey space
  • Quasi-metric measure space

ASJC Scopus subject areas

  • Applied Mathematics
  • General Mathematics

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