Domains of type 1,1 operators: a case for Triebel--Lizorkin spaces

Abstract

Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F_{p,1}^d$ to $L_p$ for $1\le p<\infty$, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin spaces. Hörmander's condition on the twisted diagonal is extended to this framework, using a general support rule for Fourier transformed pseudo-differential operators.

4 pages. Appeared in Comptes Rendu Mathematiques in 2004

Cited by in corpus (4)

• Type 1,1-operators defined by vanishing frequency modulation
• $L_p$-Theory of Type $1,1$-Operators
• Parametrices and exact paralinearisation of semi-linear boundary problems
• Fundamental Results for Pseudo-Differential Operators of Type $1,1$