The trilinear embedding theorem

• Autorzy: Hitoshi Tanaka
• Języki publikacji: EN

Abstrakty

EN

Let $σ_{i}$, i = 1,2,3, denote positive Borel measures on ℝⁿ, let 𝓓 denote the usual collection of dyadic cubes in ℝⁿ and let K: 𝓓 → [0,∞) be a map. We give a characterization of a trilinear embedding theorem, that is, of the inequality
$∑_{Q∈𝓓} K(Q)∏_{i=1}^{3} |∫_{Q} f_{i}dσ_{i}| ≤ C∏_{i=1}^{3} ||f_{i}||_{L^{p_{i}}(dσ_{i})}$
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.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 31C45: Other generalizations (nonlinear potential theory, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 3
• Strony: 239-248

Daty

wydano

2015

Twórcy

autor

Hitoshi Tanaka

• Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, 153-8914, Japan

Identyfikatory

DOI

10.4064/sm227-3-3