On the algebraic properties of the H n 2 , 1 2 spaces

Sergiu Klainerman[1]; Matei Machedon[1]

  • [1] Department of Mathematics, Princeton University, University of Maryland

Séminaire Équations aux dérivées partielles (1997-1998)

  • Volume: 1997-1998, page 1-9

Abstract

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

How to cite

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Klainerman, Sergiu, and Machedon, Matei. "On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces." Séminaire Équations aux dérivées partielles 1997-1998 (1997-1998): 1-9. <http://eudml.org/doc/10957>.

@article{Klainerman1997-1998,
abstract = {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 $H^\{\frac\{n\}\{2\}\}$.},
affiliation = {Department of Mathematics, Princeton University, University of Maryland; Department of Mathematics, Princeton University, University of Maryland},
author = {Klainerman, Sergiu, Machedon, Matei},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On the algebraic properties of the $H_\{\frac\{n\}\{2\},\{\frac\{1\}\{2\}\}\}$ spaces},
url = {http://eudml.org/doc/10957},
volume = {1997-1998},
year = {1997-1998},
}

TY - JOUR
AU - Klainerman, Sergiu
AU - Machedon, Matei
TI - On the algebraic properties of the $H_{\frac{n}{2},{\frac{1}{2}}}$ spaces
JO - Séminaire Équations aux dérivées partielles
PY - 1997-1998
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1997-1998
SP - 1
EP - 9
AB - 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 $H^{\frac{n}{2}}$.
LA - eng
UR - http://eudml.org/doc/10957
ER -

References

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  1. J. Bourgain,Fourier transform restriction phenomena for certain lattice subsets and applications to non-linear evolution equations, I, II GAFA 3(1993), 107-156, 209-262. Zbl0787.35098MR1215780
  2. Jean-Yves Chemin , Fluides Parfaits Incompressible. Asterix 230 , 1995 Zbl0829.76003MR1340046
  3. M. Escobedo and L Vega, A semilinear Dirac equation in H s ( R 3 ) for s &gt; 1 , SIAM J. Math anal. vol 28, no 2, 338-362, March 1997 Zbl0877.35028MR1434039
  4. S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math46(1993), 1221-1268 Zbl0803.35095MR1231427
  5. S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Math J. 81 (1995), 99-103 Zbl0909.35094MR1381973
  6. S. Klainerman and S. Selberg, Remark on the optimal regularity for equations of Wave Maps type, Comm.P.D.E22 (5-6), 901-918(1997). Zbl0884.35102MR1452172

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