Hp → Hp boundedness implies Hp → Lp boundedness
-
Yongsheng Han
,
Ji Li
Abstract
In this paper, we explore a general method to derive Hp → Lp boundedness from Hp → Hp boundedness of linear operators, an idea originated in the work of Han and Lu in dealing with the multiparameter flag singular integrals ([Discrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with the flag singular integrals]). These linear operators include many singular integral operators in one parameter and multiparameter settings. In this paper, we will illustrate further that this method will enable us to prove the Hp → Lp boundedness on product spaces of homogeneous type in the sense of Coifman and Weiss ([Lecture Notes in Math. 242: 1971]) where maximal function characterization of Hardy spaces is not available. Moreover, we also provide a particularly easy argument in those settings such as one parameter or multiparameter Hardy spaces 
and 
where the maximal function characterization exists. The key idea is to prove ‖ƒ‖Lp ≤ C ‖ƒ ‖Hp for ƒ ∈ Lq ∩ Hp (1 < q < ∞, 0 < p ≤ 1). It is surprising that this simple result even in this classical setting has been absent in the literature.
© de Gruyter 2011
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Artikel in diesem Heft
- The sh-Lie algebra perturbation lemma
- Gradient estimates in Orlicz spaces for nonlinear elliptic equations with BMO nonlinearity in nonsmooth domains
- Geography of non-formal symplectic and contact manifolds
- Hp → Hp boundedness implies Hp → Lp boundedness
- Global regularity for the minimal surface equation in Minkowskian geometry
- On elementarily κ-homogeneous unary structures
- Kernels, regularity and unipotent radicals in linear algebraic monoids
- Mod-Gaussian convergence: new limit theorems in probability and number theory
- Uniform large deviation for pinned hyperbolic Brownian motion
