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Intermediate weighted spaces and domains of semi-groups

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Abstract

Interpolation results of Lions (Ann Scuola Norm Sup Pisa t 13:389–403, 1959), Lions (Math Scand 9:147–177, 1961), Lions and Peetre (Publ Math IHS 19:5–68, 1964) are extended to embed domains of semi-groups into some weighted spaces studied in Artola (Bolletino UMI 5(9):125–158, 2012), Artola (Bolletino UMI, in press, 2016). Hardy’s inequality for weighted spaces (see Bolletino UMI 5(9):125–158, 2012), being necessary for the treatment, the weights are required to belong to the Hardy class \({\mathcal {H}}(p),\ (1\le p\le +\infty )\) defined in Artola (Bolletino UMI 5(9):125–158, 2012.

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Notes

  1. See [13, pp. 53–54].

  2. See [2].

  3. We refer to [7].

  4. See for example [7].

  5. We follow an adaptation of a Gagliardo method given by Lions [11] using the weights \(t^{\alpha }\), \(\alpha +1/p\in (0,1)\) which are in \({\mathcal {H}}(p)\).

  6. As for (2.25) the imbedding is only algebraically.

  7. This is an idea of Gagliardo [9].

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    Michel Artola

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Artola, M. Intermediate weighted spaces and domains of semi-groups. Ricerche mat 66, 233–257 (2017). https://doi.org/10.1007/s11587-016-0297-5

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