The trilinear embedding theorem

Hitoshi Tanaka

Hitoshi Tanaka

Studia Mathematica, Tome 231 (2015), p. 239-248 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $σ_{i}$ , i = 1,2,3, denote positive Borel measures on ℝⁿ, let denote the usual collection of dyadic cubes in ℝⁿ and let K: → [0,∞) be a map. We give a characterization of a trilinear embedding theorem, that is, of the inequality $\sum_{Q \in} K (Q) \prod_{i = 1}^{3} | \int_{Q} f_{i} d σ_{i} | \leq C \prod_{i = 1}^{3} | | f_{i} {| |}_{L^{p_{i}} (d σ_{i})}$ in terms of a discrete Wolff potential and Sawyer’s checking condition, when 1 < p₁,p₂,p₃ < ∞ and 1/p₁ + 1/p₂ + 1/p₃ ≥ 1.

Publié le : 2015-01-01

Zbl 1333.42045

EUDML-ID : urn:eudml:doc:285803

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     title = {The trilinear embedding theorem},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {239-248},
     zbl = {1333.42045},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-3-3}
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Hitoshi Tanaka. The trilinear embedding theorem. Studia Mathematica, Tome 231 (2015) pp. 239-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-3-3/