Addendum to “On the Riesz potential operator of variable order from variable exponent Morrey space to variable exponent Campanato space”, Math Meth Appl Sci. 2020; 1–8

Humberto Rafeiro, Stefan Samko

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether (Formula presented.) takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range (Formula presented.). We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper.

Original languageEnglish
Pages (from-to)557-560
Number of pages4
JournalMathematical Methods in the Applied Sciences
Volume45
Issue number1
DOIs
Publication statusPublished - Jan 15 2022

Keywords

  • BMO
  • fractional integral
  • Riesz potential
  • variable exponent Campanato spaces
  • variable exponent Morrey spaces

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering

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