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

Revista Matemática Iberoamericana (1994)

- Volume: 10, Issue: 3, page 467-505
- ISSN: 0213-2230

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topHofmann, 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 -

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