On multilinear fractional integrals

Grafakos, Loukas

Studia Mathematica, Tome 103 (1992), p. 49-56 / Harvested from The Polish Digital Mathematics Library

Résumé

In $ℝ^{n}$ , we prove $L^{p ₁} \times . . . \times L^{p_{K}}$ boundedness for the multilinear fractional integrals $I_{α} (f ₁, . . ., f_{K}) (x) = ʃ f ₁ (x - θ ₁ y) . . . f_{K} (x - θ_{K} y) {| y |}^{α - n} d y$ where the $θ_{j}$ ’s are nonzero and distinct. We also prove multilinear versions of two inequalities for fractional integrals and a multilinear Lebesgue differentiation theorem.

Publié le : 1992-01-01

Zbl 0808.42014

EUDML-ID : urn:eudml:doc:215913

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     author = {Loukas Grafakos},
     title = {On multilinear fractional integrals},
     journal = {Studia Mathematica},
     volume = {103},
     year = {1992},
     pages = {49-56},
     zbl = {0808.42014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv102i1p49bwm}
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Grafakos, Loukas. On multilinear fractional integrals. Studia Mathematica, Tome 103 (1992) pp. 49-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i1p49bwm/

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