Hwang, I. L. The \(L^ 2\)-boundedness of pseudodifferential operators. (English) Zbl 0651.35089 Trans. Am. Math. Soc. 302, 55-76 (1987). The author proves several new results of \(L^ 2\)-boundedness for pseudo differential operators a(x,D) with symbol a(x,\(\xi)\) in the classes \(S^ m_{\rho,\delta}\) of Hörmander assuming estimates for a finite number only of derivatives \(D_ x^{\alpha}D^{\beta}_{\xi}a(x,\xi)\). In particular the theorem of A. P. Calderon and R. Vaillancourt [Proc. Nat. Acad. Sci. USA 69, 1185-1187 (1972; Zbl 0244.35074)] is recaptured by using only elementary tools, as integration by parts, Fourier transform and Parseval formula. Reviewer: L.Rodino Cited in 1 ReviewCited in 62 Documents MSC: 35S05 Pseudodifferential operators as generalizations of partial differential operators 47Gxx Integral, integro-differential, and pseudodifferential operators Keywords:\(L^ 2\)-boundedness; integration by parts; Fourier transform; Parseval formula Citations:Zbl 0244.35074 PDFBibTeX XMLCite \textit{I. L. Hwang}, Trans. Am. Math. Soc. 302, 55--76 (1987; Zbl 0651.35089) Full Text: DOI