Boundedness of Monge–Ampère singular integral operators on Besov spaces

ABSTRACT

The purpose of this paper is to establish a theory of Besov spaces associated with sections under only the doubling condition on the measure and prove that Monge–Ampère singular integral operators are bounded on these spaces.

Keywords:

• Besov spaces
• Monge–Ampère singular integral operator

2010 Mathematics Subject Classifications:

• 42B20
• 42B35

Acknowledgments

The authors would like to express their gratitude to the referee for his/her comments and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second and third authors are supported by Ministry of Science and Technology, R.O.C. [grant numbers #MOST 106-2115-M-008-003-MY2 and #MOST 106-2115-M-008-004-MY3], respectively, as well as supported by National Center for Theoretical Sciences of Taiwan.