Orobitg, Joan On spectral synthesis in some Hardy-Sobolev spaces. (English) Zbl 0794.46023 Proc. R. Ir. Acad., Sect. A 92, No. 2, 205-223 (1992). The Hardy-Sobolev spaces to be considered are the potential spaces \(I_ s H^ 1=\{f: f=I_ s *h, h\in H^ 1\}\), \(0< s\leq d\), where \(I_ s\) is the Riesz potential of order \(s\), that is, \(I_ s(x)= | x|^{s- d}\) \((=\log| x|\) if \(s=d)\) and \(H^ 1\) is the usual Fefferman- Stein Hardy space. We endow, \(I_ sH^ 1\) with the Banach space norm \(\| f\|= \| h\|_{H^ 1}\), \(f= I_ s* h\). In this paper, we give a necessary and sufficient condition so that a function \(f\) can be approximated in \(I_ s H^ 1\), \(0< s<2\), by functions in \(C^ \infty_ 0(F^ c)\), where \(F\) is a closed set of \(\mathbb{R}^ d\). Reviewer: J.Orobitg (Barcelona) Cited in 1 Document MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces 43A45 Spectral synthesis on groups, semigroups, etc. Keywords:Hardy-Sobolev spaces; potential spaces; Riesz potential; Fefferman-Stein Hardy space PDFBibTeX XMLCite \textit{J. Orobitg}, Proc. R. Ir. Acad., Sect. A 92, No. 2, 205--223 (1992; Zbl 0794.46023)