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 Fdp,1 to Lp for 1 p<∞, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin spaces. H\"ormander's condition on the twisted diagonal is extended to this framework, using a general support rule for Fourier transformed pseudo-differential operators.
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