Science in China Series A: Mathematics

, 52:1042

Orlicz-Hardy spaces associated with operators

Article

DOI: 10.1007/s11425-008-0136-6

Cite this article as:
Jiang, R., Yang, D. & Zhou, Y. Sci. China Ser. A-Math. (2009) 52: 1042. doi:10.1007/s11425-008-0136-6

Abstract

Let L be a linear operator in L2 (ℝn) and generate an analytic semigroup {etL}t⩾0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper type 1 and of critical lower type po(ω) ∂ (n/(n+θ(L)),1] and ρ(t) = tt1/ω−1(t−1) for t ∈ (0,∞). We introduce the Orlicz-Hardy space Hω, L (ℝn) and the BMO-type space BMOρ, L (ℝn) and establish the John-Nirenberg inequality for BMOρ, L (ℝn) functions and the duality relation between Hω, L ((ℝn) and BMOρ, L* (ℝn), where L* denotes the adjoint operator of L in L2 (ℝn). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMOρ, L* (ℝn) and the molecular characterization of Hω, L (ℝn); the latter is used to establish the boundedness of the generalized fractional operator Lργ from Hω, L (ℝn) to HL1 (ℝn) or Lq (ℝn) with certain q > 1, where HL (ℝn) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = tp for t ∈ (0,∞) and p ∈ (n/(n + θ(L)), 1].

Keywords

Orlicz functionOrlicz-Hardy spaceBMOdualitymoleculefractional integral

MSC(2000)

42B3042B3542B2042B25

Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems, Ministry of EducationSchool of Mathematical Sciences, Beijing Normal UniversityBeijingChina