Weighted norm inequalities for pseudo-pseudodifferential operators defined by amplitudes (Q973955)

Conditions for \(L^p\)-boundedness of pseudodifferential operators whose symbols are only measurable and essentially bounded in the spatial variables were found by \textit{C.\,E.\thinspace Kenig} and \textit{W.\,Staubach} [Stud.\ Math.\ 183, No.\,3, 249--258 (2007; Zbl 1178.35397)]. The authors of the paper under review extend those results in a number of directions -- they prove weighted norm inequalities, consider operators defined by amplitudes, show how to improve the results for the case where a symbol or amplitude contains certain types of factors oscillating with respect to the dual variables [see also \textit{S.\,Chanillo} and \textit{A.\,Torchinsky}, Ark.\ Mat.\ 24, 1--25 (1986; Zbl 0609.35085)]. As an application, the authors use their weighted norm inequalities to prove the boundedness of commutators of the above pseudodifferential operators with functions of bounded mean oscillation.