On the Boundedness and Compactness of Nonregular Pseudo‐Differential Operators

Abstract

Abstract We study the boundedness properties of nonregular pseudo‐differential operators and their adjoints on Triebel spaces F , 0 < p, q≦ ∞. Special attention is payed to sharp estimates. The second aim of this paper is the compactness properties of these operators on weighted and unweighted Triebel spaces F (w) where the weight w may belong to an arbitrary Muckenhoupt class A ∞ .