Rs-sectorial operators and generalized Triebel-Lizorkin spaces

2012/07/17 by Kunstmann, Peer Christian, Ullmann, Alexander
#42B25 (Secondary) #46E30 #47A60 #47B38 (Primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1207.4217

Abstract

We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of R_s-sectorial operators, which in turn is based on the notion of R_s-bounded sets of operators introduced by Lutz Weis, we obtain a neat theory including equivalence of various norms and a precise description of real and complex interpolation spaces. Another main result of this article is that an R_s-sectorial operator always has a bounded H^∞-functional calculus in its associated generalized Triebel-Lizorkin spaces.

Related

• Operator-valued Triebel-Lizorkin spaces
• New properties of the multivariable H^∞ functional calculus of sectorial operators
• The H^∞-calculus and sums of closed operators
• Functional calculi for sectorial operators and related function theory
• Two types of Rubio de Francia operators on Triebel--Lizorkin and Besov spaces