Phong, D. H.; Stein, Elias M. Singular integrals related to the Radon transform and boundary value problems. (English) Zbl 0567.42010 Proc. Natl. Acad. Sci. USA 80, 7697-7701 (1983). Let \(\Omega\) be a manifold without boundary and assume that through each point P in \(\Omega\) passes a hypersurface \(\Omega_ P\) that carries a singular density \(K_ P\). Given a function u, the singular Radon transform of u is the new function on \(\Omega\), whose value at P is the integral on \(\Omega_ P\) of u against \(K_ P\). Examples and applications arising from integral geometry and several complex variables are discussed. Reviewer: F.Natterer Cited in 2 ReviewsCited in 20 Documents MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 58J40 Pseudodifferential and Fourier integral operators on manifolds 44A15 Special integral transforms (Legendre, Hilbert, etc.) Keywords:Hilbert integral; manifold without boundary; hypersurface; singular density; Radon transform PDFBibTeX XMLCite \textit{D. H. Phong} and \textit{E. M. Stein}, Proc. Natl. Acad. Sci. USA 80, 7697--7701 (1983; Zbl 0567.42010) Full Text: DOI