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

1 Citation (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
JournalRicerche di Matematica
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Campanato space
  • Fractional operator
  • Morrey space
  • Quasi-metric measure space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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