TY - JOUR
T1 - VMO spaces associated with operators with Gaussian upper bounds on product domains
AU - Bui, The Anh
AU - Duong, Xuan Thinh
AU - Li, Ji
PY - 2017
Y1 - 2017
N2 - In this paper, we extend the well-known result "the predual of Hardy space H1 is VMO" to the product setting, associated with differential operators. Let Li, i = 1, 2, be the infinitesimal generators of the analytic semigroups {e-tLi} on L2(ℝ). Assume that the kernels of the semigroups {e-tLi} satisfy the Gaussian upper bounds. We introduce the VMO spaces VMOL1,L2(ℝ × ℝ) associated with operators L1 and L2 on the product domain ℝ × ℝ, then show that the dual space of VMOL1,L2(ℝ × ℝ) is the Hardy space H1L1∗,L2∗ (ℝ × ℝ) associated with the adjoint operators L1∗ and L2∗.
AB - In this paper, we extend the well-known result "the predual of Hardy space H1 is VMO" to the product setting, associated with differential operators. Let Li, i = 1, 2, be the infinitesimal generators of the analytic semigroups {e-tLi} on L2(ℝ). Assume that the kernels of the semigroups {e-tLi} satisfy the Gaussian upper bounds. We introduce the VMO spaces VMOL1,L2(ℝ × ℝ) associated with operators L1 and L2 on the product domain ℝ × ℝ, then show that the dual space of VMOL1,L2(ℝ × ℝ) is the Hardy space H1L1∗,L2∗ (ℝ × ℝ) associated with the adjoint operators L1∗ and L2∗.
KW - Hardy spaces
KW - VMO spaces
KW - Tent spaces
KW - Product domains
UR - http://www.scopus.com/inward/record.url?scp=84969940982&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP140100649
UR - http://purl.org/au-research/grants/arc/DP160100153
U2 - 10.1007/s12220-016-9710-2
DO - 10.1007/s12220-016-9710-2
M3 - Article
AN - SCOPUS:84969940982
VL - 27
SP - 1065
EP - 1085
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 2
ER -