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On traces spaces connected with a class of intermediate weighted spaces

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Abstract

Methods developed by Lions and Peetre (Pub Math de l’IHES 19:5–68, 1964) are used to extend results derived in Artola (Bolletino UMI (9) V:125–158, 2012) for traces of weighted spaces. The weights are required to belong to the Hardy class H(p) defined in Artola (Bolletino UMI (9) V:125–158, 2012) to ensure that a necessary convolution product remains valid in weighted spaces. The restriction, apparently new, is necessary for the present treatment.

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Notes

  1. My thesis on Partial Differential Equations with delay was published in 1969 at the Annals of E.N.Sup.ULM Paris.

  2. See [16] and the bibliography therein.

  3. Pf = Finite Part at the sense of Laurent Schwartz [29].

  4. See Theorem 3.3 of [6].

  5. See [22–24].

  6. See also [31] for unweighted spaces.

  7. For the convenience of the Reader we adapt the proof given in [10].

  8. As noticed by J. Peetre.

  9. See also Tartar [31].

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  1. 27, Avenue du Ribeyrot, 33610, Cestas, France

    Michel Artola

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  1. Michel Artola
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Correspondence to Michel Artola.

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In memory of Jacques-Louis Lions, 1928–2001.

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Artola, M. On traces spaces connected with a class of intermediate weighted spaces. Boll Unione Mat Ital 10, 241–269 (2017). https://doi.org/10.1007/s40574-016-0079-8

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