Elliptic functions, area integrals and the exponential square class on B₁(0) ⊆ ℝⁿ, n > 2

Caroline Sweezy. "Elliptic functions, area integrals and the exponential square class on B₁(0) ⊆ ℝⁿ, n > 2." Studia Mathematica 164.1 (2004): 1-28. <http://eudml.org/doc/284424>.

@article{CarolineSweezy2004,
abstract = {For two strictly elliptic operators L₀ and L₁ on the unit ball in ℝⁿ, whose coefficients have a difference function that satisfies a Carleson-type condition, it is shown that a pointwise comparison concerning Lusin area integrals is valid. This result is used to prove that if L₁u₁ = 0 in B₁(0) and $Su₁ ∈ L^\{∞\}(S^\{n-1\})$ then $u₁|_\{S^\{n-1\}\} = f$ lies in the exponential square class whenever L₀ is an operator so that L₀u₀ = 0 and $Su₀ ∈ L^\{∞\}$ implies $u₀|_\{S^\{n-1\}\}$ is in the exponential square class; here S is the Lusin area integral. The exponential square theorem, first proved by Thomas Wolff for harmonic functions in the upper half-space, is proved on B₁(0) for constant coefficient operator solutions, thus giving a family of operators for L₀. Methods of proof include martingales and stopping time arguments.},
author = {Caroline Sweezy},
journal = {Studia Mathematica},
language = {eng},
number = {1},
pages = {1-28},
title = {Elliptic functions, area integrals and the exponential square class on B₁(0) ⊆ ℝⁿ, n > 2},
url = {http://eudml.org/doc/284424},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Caroline Sweezy
TI - Elliptic functions, area integrals and the exponential square class on B₁(0) ⊆ ℝⁿ, n > 2
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 1
SP - 1
EP - 28
AB - For two strictly elliptic operators L₀ and L₁ on the unit ball in ℝⁿ, whose coefficients have a difference function that satisfies a Carleson-type condition, it is shown that a pointwise comparison concerning Lusin area integrals is valid. This result is used to prove that if L₁u₁ = 0 in B₁(0) and $Su₁ ∈ L^{∞}(S^{n-1})$ then $u₁|_{S^{n-1}} = f$ lies in the exponential square class whenever L₀ is an operator so that L₀u₀ = 0 and $Su₀ ∈ L^{∞}$ implies $u₀|_{S^{n-1}}$ is in the exponential square class; here S is the Lusin area integral. The exponential square theorem, first proved by Thomas Wolff for harmonic functions in the upper half-space, is proved on B₁(0) for constant coefficient operator solutions, thus giving a family of operators for L₀. Methods of proof include martingales and stopping time arguments.
LA - eng
UR - http://eudml.org/doc/284424
ER -