Regularity properties of singular integral operators
Studia Mathematica, Tome 119 (1996) no. 3, p. 199.
Voir la notice de l'article dans European Digital Mathematics Library
For s>0, we consider bounded linear operators from
D
(
ℝ
n
)
into
D
'
(
ℝ
n
)
whose kernels K satisfy the conditions
|
∂
x
γ
K
(
x
,
y
)
|
≤
C
γ
|
x
-
y
|
-
n
+
s
-
|
γ
|
for x≠y, |γ|≤ [s]+1,
|
∇
y
∂
x
γ
K
(
x
,
y
)
|
≤
C
γ
|
x
-
y
|
-
n
+
s
-
|
γ
|
-
1
for |γ|=[s], x≠y. We establish a new criterion for the boundedness of these operators from
L
2
(
ℝ
n
)
into the homogeneous Sobolev space
Ḣ
s
(
ℝ
n
)
. This is an extension of the well-known T(1) Theorem due to David and Journé. Our arguments make use of the function T(1) and the BMO-Sobolev space. We give some applications to the Besov and Triebel-Lizorkin spaces as well as some other potential spaces.
Classification :
46E35, 42B20, 42B30
Mots-clés : Besov spaces, regularity, singular integral operators, Theorem, BMO-Sobolev space, Triebel-Lizorkin spaces
Mots-clés : Besov spaces, regularity, singular integral operators, Theorem, BMO-Sobolev space, Triebel-Lizorkin spaces
@article{STUMA_1996__119_3_216296,
author = {Abdellah Youssfi},
title = {Regularity properties of singular integral operators},
journal = {Studia Mathematica},
pages = {199},
publisher = {mathdoc},
volume = {119},
number = {3},
year = {1996},
zbl = {0857.42008},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/STUMA_1996__119_3_216296/}
}
Abdellah Youssfi. Regularity properties of singular integral operators. Studia Mathematica, Tome 119 (1996) no. 3, p. 199. https://geodesic-test.mathdoc.fr/item/STUMA_1996__119_3_216296/