Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions

David Mascré

Colloquium Mathematicae (2006)

  • Volume: 105, Issue: 1, page 77-104
  • ISSN: 0010-1354

Abstract

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On a metric measure space (X,ϱ,μ), consider the weight functions w α ( x ) = ϱ ( x , z ₀ ) - α ₀ if ϱ(x,z₀) < 1, w α ( x ) = ϱ ( x , z ₀ ) - α ₁ if ϱ(x,z₀) ≥ 1, w β ( x ) = ϱ ( x , z ₀ ) - β ₀ if ϱ(x,z₀) < 1, w β ( x ) = ϱ ( x , z ₀ ) - β ₁ if ϱ(x,z₀) ≥ 1, where z₀ is a given point of X, and let κ a : X × X → ℝ ₊ be an operator kernel satisfying κ a ( x , y ) ≤ c ϱ ( x , y ) a - d for all x,y ∈ X such that ϱ(x,y) < 1, κ a ( x , y ) ≤ c ϱ ( x , y ) a - D for all x,y ∈ X such that ϱ(x,y)≥ 1, where 0 < a < min(d,D), and d and D are respectively the local and global volume growth rate of the space X. We determine conditions on a, α₀, α₁, β₀, β₁ ∈ ℝ for the Hardy-Littlewood-Sobolev operator with kernel κ ( x , y ) = w β ( x ) κ a ( x , y ) w α ( y ) to be bounded from L p ( X ) to L q ( X ) for 1 < p ≤ q < ∞.

How to cite

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David Mascré. "Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions." Colloquium Mathematicae 105.1 (2006): 77-104. <http://eudml.org/doc/286131>.

@article{DavidMascré2006,
author = {David Mascré},
journal = {Colloquium Mathematicae},
keywords = {metric measure space; Vitali space; Hardy-Littlewood-Sobolev inequality},
language = {fre},
number = {1},
pages = {77-104},
title = {Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions},
url = {http://eudml.org/doc/286131},
volume = {105},
year = {2006},
}

TY - JOUR
AU - David Mascré
TI - Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 1
SP - 77
EP - 104
LA - fre
KW - metric measure space; Vitali space; Hardy-Littlewood-Sobolev inequality
UR - http://eudml.org/doc/286131
ER -

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