TY - JOUR
T1 - Classes Of hardy spaces associated with operators, duality theorem and applications
AU - Yan, Lixin
PY - 2008/8
Y1 - 2008/8
N2 - Let L be the infinitesimal generator of an analytic semigroup on L 2(ℝn) with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space H1L (ℝn) and a BMOl(ℝn) space associated with the operator L were introduced and studied. In this paper we define a class of Hp/L(ℝn) spaces associated with the operator L for a range of p < 1 acting on certain spaces of Morrey-Campanato functions defined in New Morrey-Campanato spaces associated with operators and applications by Duong and Yan (2005), and they generalize the classical Hp/l(ℝn) spaces. We then establish a duality theorem between the Hp L(ℝn) spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on Hp/L(ℝn) and give the inclusion between the classical H p(ℝn) spaces and the Hp/L(ℝn) spaces associated with operators.
AB - Let L be the infinitesimal generator of an analytic semigroup on L 2(ℝn) with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space H1L (ℝn) and a BMOl(ℝn) space associated with the operator L were introduced and studied. In this paper we define a class of Hp/L(ℝn) spaces associated with the operator L for a range of p < 1 acting on certain spaces of Morrey-Campanato functions defined in New Morrey-Campanato spaces associated with operators and applications by Duong and Yan (2005), and they generalize the classical Hp/l(ℝn) spaces. We then establish a duality theorem between the Hp L(ℝn) spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on Hp/L(ℝn) and give the inclusion between the classical H p(ℝn) spaces and the Hp/L(ℝn) spaces associated with operators.
UR - http://www.scopus.com/inward/record.url?scp=67349118076&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-08-04476-0
DO - 10.1090/S0002-9947-08-04476-0
M3 - Article
AN - SCOPUS:67349118076
VL - 360
SP - 4383
EP - 4408
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -