On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces

Klainerman, Sergiu; Machedon, Matei

On the algebraic properties of the

H_{\frac{n}{2}, \frac{1}{2}}

spaces

Klainerman, Sergiu ¹ ; Machedon, Matei ¹

¹ Department of Mathematics, Princeton University, University of Maryland

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 7, 9 p.

Résumé

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

MR Zbl

Affiliations des auteurs :

Klainerman, Sergiu ¹ ; Machedon, Matei ¹

¹ Department of Mathematics, Princeton University, University of Maryland

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     author = {Klainerman, Sergiu and Machedon, Matei},
     title = {On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:7},
     pages = {1--9},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1997-1998},
     zbl = {1064.46501},
     mrnumber = {1660520},
     language = {en},
     url = {https://www.numdam.org/item/SEDP_1997-1998____A7_0/}
}

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Klainerman, Sergiu; Machedon, Matei. On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1997-1998), Exposé no. 7, 9 p. https://www.numdam.org/item/SEDP_1997-1998____A7_0/

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