TY - JOUR
T1 - Hardy and BMO spaces associated to divergence form elliptic operators
AU - Hofmann, Steve
AU - Mayboroda, Svitlana
N1 - Funding Information:
S. Hofmann was supported by the National Science Foundation.
PY - 2009/2
Y1 - 2009/2
N2 - Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy and BMO spaces, and a John-Nirenberg inequality.
AB - Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy and BMO spaces, and a John-Nirenberg inequality.
KW - 35J15
KW - 42B25
KW - 42B30
KW - 42B35
UR - http://www.scopus.com/inward/record.url?scp=70449088739&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70449088739&partnerID=8YFLogxK
U2 - 10.1007/s00208-008-0295-3
DO - 10.1007/s00208-008-0295-3
M3 - Article
AN - SCOPUS:70449088739
SN - 0025-5831
VL - 344
SP - 37
EP - 116
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1
ER -