Monge–Ampère singular integral operators acting on Triebel–Lizorkin spaces

Abstract

We study the Triebel–Lizorkin spaces associated with sections which are closely related to the Monge-Ampère equations and show that Monge-Ampère singular integral operators are bounded on these Triebel–Lizorkin spaces.

COMMUNICATED BY:

• Jen-Chih Yao

Keywords:

• Triebel–Lizorkin spaces
• Monge-Ampère singular integral operators

2010 Mathematics Subject Classifications:

• 42B20
• 42B35

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NNSF of China [grant numbers 11771223 and 11201003] and University NSR Project of Anhui Province [grant number KJ2017ZD27]; MOST of Taiwan [grant number #MOST 106-2115-M-008-003-MY2] and NCTS of Taiwan; MOST of Taiwan [grant number #MOST 106-2115-M-008-004-MY3] and NCTS of Taiwan; NNSF of China [grant number 11471033], NSF of Anhui Provincial [grant number 1408085MA01], and University NSR Project of Anhui Province [grant number KJ2014A087].