A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.

Tolsa, Xavier. "A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.." Publicacions Matemàtiques 45.1 (2001): 163-174. <http://eudml.org/doc/41420>.

@article{Tolsa2001,
abstract = {Given a doubling measure μ on Rd, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L2(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition adapted to the non doubling situation.},
author = {Tolsa, Xavier},
journal = {Publicacions Matemàtiques},
keywords = {Medida de Radon; Integrales singulares; Función armónica; non doubling measures; non homogeneous spaces; weak estimates; singular integrals; Calderón-Zygmund operators; Calderón-Zygmund decomposition},
language = {eng},
number = {1},
pages = {163-174},
title = {A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.},
url = {http://eudml.org/doc/41420},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Tolsa, Xavier
TI - A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 1
SP - 163
EP - 174
AB - Given a doubling measure μ on Rd, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L2(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition adapted to the non doubling situation.
LA - eng
KW - Medida de Radon; Integrales singulares; Función armónica; non doubling measures; non homogeneous spaces; weak estimates; singular integrals; Calderón-Zygmund operators; Calderón-Zygmund decomposition
UR - http://eudml.org/doc/41420
ER -