The trilinear embedding theorem

Hitoshi Tanaka. "The trilinear embedding theorem." Studia Mathematica 227.3 (2015): 239-248. <http://eudml.org/doc/285803>.

@article{HitoshiTanaka2015,
abstract = {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 $∑_\{Q∈\} K(Q)∏_\{i=1\}^\{3\} |∫_\{Q\} f_\{i\}dσ_\{i\}| ≤ C∏_\{i=1\}^\{3\} ||f_\{i\}||_\{L^\{p_\{i\}\}(dσ_\{i\})\}$ 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.},
author = {Hitoshi Tanaka},
journal = {Studia Mathematica},
keywords = {trilinear embedding theorem; discrete Wolff potential; bilinear positive dyadic operator; Sawyer's checking condition; two-weight trace inequality},
language = {eng},
number = {3},
pages = {239-248},
title = {The trilinear embedding theorem},
url = {http://eudml.org/doc/285803},
volume = {227},
year = {2015},
}

TY - JOUR
AU - Hitoshi Tanaka
TI - The trilinear embedding theorem
JO - Studia Mathematica
PY - 2015
VL - 227
IS - 3
SP - 239
EP - 248
AB - 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 $∑_{Q∈} K(Q)∏_{i=1}^{3} |∫_{Q} f_{i}dσ_{i}| ≤ C∏_{i=1}^{3} ||f_{i}||_{L^{p_{i}}(dσ_{i})}$ 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.
LA - eng
KW - trilinear embedding theorem; discrete Wolff potential; bilinear positive dyadic operator; Sawyer's checking condition; two-weight trace inequality
UR - http://eudml.org/doc/285803
ER -