Interpolation of quasicontinuous functions

Joan Cerdà; Joaquim Martín; Pilar Silvestre

Joan Cerdà ; Joaquim Martín ; Pilar Silvestre

Banach Center Publications, Tome 95 (2011), p. 281-286 / Harvested from The Polish Digital Mathematics Library

Résumé

If C is a capacity on a measurable space, we prove that the restriction of the K-functional $K (t, f; L^{p} (C), L^{\infty} (C))$ to quasicontinuous functions f ∈ QC is equivalent to $K (t, f; L^{p} (C) \cap Q C, L^{\infty} (C) \cap Q C)$ . We apply this result to identify the interpolation space ${(L^{p ₀, q ₀} (C) \cap Q C, L^{p ₁, q ₁} (C) \cap Q C)}_{θ, q}$ .

Publié le : 2011-01-01

Zbl 1243.46009

EUDML-ID : urn:eudml:doc:282488

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     author = {Joan Cerd\`a and Joaquim Mart\'\i n and Pilar Silvestre},
     title = {Interpolation of quasicontinuous functions},
     journal = {Banach Center Publications},
     volume = {95},
     year = {2011},
     pages = {281-286},
     zbl = {1243.46009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-15}
}

Joan Cerdà; Joaquim Martín; Pilar Silvestre. Interpolation of quasicontinuous functions. Banach Center Publications, Tome 95 (2011) pp. 281-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-15/