On singular integrals of Calderón-type in Rn and BMO.

Hofmann, Steve. "On singular integrals of Calderón-type in Rn and BMO.." Revista Matemática Iberoamericana 10.3 (1994): 467-505. <http://eudml.org/doc/39463>.

@article{Hofmann1994,
abstract = {We prove Lp (and weighted Lp) bounds for singular integrals of the formp.v.  ∫Rn E (A(x) - A(y) / |x - y|) (Ω(x - y) / |x - y|n) f(y) dy,where E(t) = cos t if Ω is odd, and E(t) = sin t if Ω is even, and where ∇ A ∈ BMO. Even in the case that Ω is smooth, the theory of singular integrals with rough kernels plays a key role in the proof. By standard techniques, the trigonometric function E can then be replaced by a large class of smooth functions F. Some related operators are also considered. As a further application we prove a compactness result for certain layer potentials.},
author = {Hofmann, Steve},
journal = {Revista Matemática Iberoamericana},
keywords = {Integrales singulares; Análisis de Fourier; singular integrals of Calderón-type; BMO; compactness; layer potentials},
language = {eng},
number = {3},
pages = {467-505},
title = {On singular integrals of Calderón-type in Rn and BMO.},
url = {http://eudml.org/doc/39463},
volume = {10},
year = {1994},
}

TY - JOUR
AU - Hofmann, Steve
TI - On singular integrals of Calderón-type in Rn and BMO.
JO - Revista Matemática Iberoamericana
PY - 1994
VL - 10
IS - 3
SP - 467
EP - 505
AB - We prove Lp (and weighted Lp) bounds for singular integrals of the formp.v.  ∫Rn E (A(x) - A(y) / |x - y|) (Ω(x - y) / |x - y|n) f(y) dy,where E(t) = cos t if Ω is odd, and E(t) = sin t if Ω is even, and where ∇ A ∈ BMO. Even in the case that Ω is smooth, the theory of singular integrals with rough kernels plays a key role in the proof. By standard techniques, the trigonometric function E can then be replaced by a large class of smooth functions F. Some related operators are also considered. As a further application we prove a compactness result for certain layer potentials.
LA - eng
KW - Integrales singulares; Análisis de Fourier; singular integrals of Calderón-type; BMO; compactness; layer potentials
UR - http://eudml.org/doc/39463
ER -