Complex interpolation on variable exponent Campanato spaces of order k

Abstract

In this paper, we show the validity of a Riesz–Thorin type interpolation theorem for linear operators acting from variable exponent Lebesgue spaces into variable exponent Campanato spaces of order k.

Keywords:

• Riesz–Thorin interpolation theorem
• complex interpolation
• variable exponent spaces
• Campanato spaces

AMS Subject Classifications:

• 46E30
• 46B70

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first named author was supported by the Shota Rustaveli National Science Foundation grant (Contract Numbers: D/13-23 and 31/47). The second named author was partially supported by research project “Study of boundedness of operators in generalized Morrey spaces”, ID-PRJ: 6576 of the Faculty of Sciences of Pontificia Universidad Javeriana, Bogotá, Colombia. The third named author was supported by Pontificia Universidad Javeriana, Bogotá, Colombia as Post-Doctoral Investigator working on the research project “Study of boundedness of some operators in generalized Morrey spaces”, ID-PRJ: 6576 (Contract Number: DPE-040-15).