The continuity of pseudo-differential operators on weighted local Hardy spaces

Ming-Yi Lee, Chin-Cheng Lin, and Ying-Chieh Lin. "The continuity of pseudo-differential operators on weighted local Hardy spaces." Studia Mathematica 198.1 (2010): 69-77. <http://eudml.org/doc/285669>.

@article{Ming2010,
abstract = {We first show that a linear operator which is bounded on $L²_\{w\}$ with w ∈ A₁ can be extended to a bounded operator on the weighted local Hardy space $h¹_\{w\}$ if and only if this operator is uniformly bounded on all $h¹_\{w\}$-atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to $h¹_\{w\}$.},
author = {Ming-Yi Lee, Chin-Cheng Lin, Ying-Chieh Lin},
journal = {Studia Mathematica},
keywords = {pseudo-differential operators; Muckenhoupt weights; local Hardy spaces},
language = {eng},
number = {1},
pages = {69-77},
title = {The continuity of pseudo-differential operators on weighted local Hardy spaces},
url = {http://eudml.org/doc/285669},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Ming-Yi Lee
AU - Chin-Cheng Lin
AU - Ying-Chieh Lin
TI - The continuity of pseudo-differential operators on weighted local Hardy spaces
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 1
SP - 69
EP - 77
AB - We first show that a linear operator which is bounded on $L²_{w}$ with w ∈ A₁ can be extended to a bounded operator on the weighted local Hardy space $h¹_{w}$ if and only if this operator is uniformly bounded on all $h¹_{w}$-atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to $h¹_{w}$.
LA - eng
KW - pseudo-differential operators; Muckenhoupt weights; local Hardy spaces
UR - http://eudml.org/doc/285669
ER -