A₁-regularity and boundedness of Calderón-Zygmund operators

Dmitry V. Rutsky. "A₁-regularity and boundedness of Calderón-Zygmund operators." Studia Mathematica 221.3 (2014): 231-247. <http://eudml.org/doc/286107>.

@article{DmitryV2014,
abstract = {The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and X'.},
author = {Dmitry V. Rutsky},
journal = {Studia Mathematica},
keywords = {-regularity; Calderón-Zygmund operator; Hardy-Littlewood maximal operator},
language = {eng},
number = {3},
pages = {231-247},
title = {A₁-regularity and boundedness of Calderón-Zygmund operators},
url = {http://eudml.org/doc/286107},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Dmitry V. Rutsky
TI - A₁-regularity and boundedness of Calderón-Zygmund operators
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 3
SP - 231
EP - 247
AB - The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and X'.
LA - eng
KW - -regularity; Calderón-Zygmund operator; Hardy-Littlewood maximal operator
UR - http://eudml.org/doc/286107
ER -