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On the algebraic properties of the \(H_{n/2,1/2}\) spaces. (English) Zbl 1064.46501

Summary: We investigate the multiplicative properties of the spaces \(H^{{n\over 2},{1\over 2}}\). As in the case of the classical Sobolev spaces \(H^{{n\over 2}}\), this space does not form an algebra. We investigate instead the space \(H^{{n\over 2}}\cap L^\infty\), more precisely, a subspace of it formed by products of solutions of the homogeneous wave equation with data in \(H^{{n\over 2}}\).

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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