TY - JOUR
T1 - Weighted hardy spaces associated with operators satisfying reinforced off-diagonal estimates
AU - Bui, The Anh
AU - Cao, Jun
AU - Ky, Luong Dang
AU - Yang, Dachun
AU - Yang, Sibei
PY - 2013/7/23
Y1 - 2013/7/23
N2 - Let L be a nonnegative self-adjoint operator on L2(ℝn) satisfying the reinforced (pl,p'l) off-diagonal estimates, where pl [1,2) and p'L denotes its conjugate exponent. Assume that p (0,1] and the weight w satisfies the reverse Hölder inequality of order (p'L/p)'. In particular, if the heat kernels of the semigroups {e~tL}t>0 satisfy the Gaussian upper bounds, thenpL = 1 and hence w G A00(ℝn). In this paper, the authors introduce the weighted Hardy spaces Hp L w(ℝn) associated with the operator L, via the Lusin area function associated with the heat semigroup generated by L. Characterizations of Hp L w (ℝn), in terms of the atom and the molecule, are obtained. As applications, the bounded-ness of singular integrals such as spectral multipliers, square functions and Riesz transforms on weighted Hardy spaces HL p w(ℝn) are investigated. Even for the Schrödinger operator - Δ + V with 0 < V e L1oc(ℝn), the obtained results in this paper essentially improve the known results by extending the narrow range of the weights into the whole A∞(Rn) weights.
AB - Let L be a nonnegative self-adjoint operator on L2(ℝn) satisfying the reinforced (pl,p'l) off-diagonal estimates, where pl [1,2) and p'L denotes its conjugate exponent. Assume that p (0,1] and the weight w satisfies the reverse Hölder inequality of order (p'L/p)'. In particular, if the heat kernels of the semigroups {e~tL}t>0 satisfy the Gaussian upper bounds, thenpL = 1 and hence w G A00(ℝn). In this paper, the authors introduce the weighted Hardy spaces Hp L w(ℝn) associated with the operator L, via the Lusin area function associated with the heat semigroup generated by L. Characterizations of Hp L w (ℝn), in terms of the atom and the molecule, are obtained. As applications, the bounded-ness of singular integrals such as spectral multipliers, square functions and Riesz transforms on weighted Hardy spaces HL p w(ℝn) are investigated. Even for the Schrödinger operator - Δ + V with 0 < V e L1oc(ℝn), the obtained results in this paper essentially improve the known results by extending the narrow range of the weights into the whole A∞(Rn) weights.
UR - http://www.scopus.com/inward/record.url?scp=84880796647&partnerID=8YFLogxK
U2 - 10.11650/tjm.17.2013.2719
DO - 10.11650/tjm.17.2013.2719
M3 - Article
AN - SCOPUS:84880796647
SN - 1027-5487
VL - 17
SP - 1127
EP - 1166
JO - Taiwanese Journal of Mathematics
JF - Taiwanese Journal of Mathematics
IS - 4
ER -