Boundedness of para-product operators on spaces of homogeneous type

Xiao, Yayuan. "Boundedness of para-product operators on spaces of homogeneous type." Czechoslovak Mathematical Journal 67.1 (2017): 235-252. <http://eudml.org/doc/287884>.

@article{Xiao2017,
abstract = {We obtain the boundedness of Calderón-Zygmund singular integral operators $T$ of non-convolution type on Hardy spaces $H^p(\mathcal \{X\})$ for $ 1/\{(1+\epsilon )\}<p\le 1$, where $\{\mathcal \{X\}\}$ is a space of homogeneous type in the sense of Coifman and Weiss (1971), and $\epsilon $ is the regularity exponent of the kernel of the singular integral operator $T$. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature.},
author = {Xiao, Yayuan},
journal = {Czechoslovak Mathematical Journal},
keywords = {boundedness; Calderón-Zygmund singular integral operator; para-product; spaces of homogeneous type},
language = {eng},
number = {1},
pages = {235-252},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of para-product operators on spaces of homogeneous type},
url = {http://eudml.org/doc/287884},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Xiao, Yayuan
TI - Boundedness of para-product operators on spaces of homogeneous type
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 235
EP - 252
AB - We obtain the boundedness of Calderón-Zygmund singular integral operators $T$ of non-convolution type on Hardy spaces $H^p(\mathcal {X})$ for $ 1/{(1+\epsilon )}<p\le 1$, where ${\mathcal {X}}$ is a space of homogeneous type in the sense of Coifman and Weiss (1971), and $\epsilon $ is the regularity exponent of the kernel of the singular integral operator $T$. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature.
LA - eng
KW - boundedness; Calderón-Zygmund singular integral operator; para-product; spaces of homogeneous type
UR - http://eudml.org/doc/287884
ER -