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| 1 | Maximal function characterizations of Hardy spaces on RD-spaces and their applications显示文摘Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a 'dimension' n. For α∈ (0, ∞) denote by Hαp(X ), Hdp(X ), and H?,p(X ) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calder′on reproducing formula, it is shown that all these Hardy spaces coincide with Lp(X ) when p ∈ (1, ∞] and with each other when p ∈ (n/(n + 1), 1]. An atomic characterization for H*,p(X ) with p ∈ (n/(n + 1), 1] is also established; moreover, in the range p ∈ (n/(n + 1), 1], it is proved that the space H?,p(X ), the Hardy space Hp(X ) defined via the Littlewood-Paley function, and the atomic Hardy space of Coifman and Weiss coincide. Furthermore, it is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from Hp(X ) to some quasi-Banach space B if and only if T maps all (p, q)-atoms when q ∈ (p, ∞)∩[1, ∞) or continuous (p, ∞)-atoms into uniformly bounded elements of B. | Loukas GRAFAKOS | 2008 | Science China Mathematics2008，51，12： | 10 |
| 2 | Boundedness of paraproduct operators on RD-spaces显示文摘Let(X,d,μ) be an RD-space with 'dimension' n,namely,a space of homogeneous type in the sense of Coifman and Weiss satisfying a certain reverse doubling condition.Using the Calder'on reproducing formula,the authors hereby establish boundedness for paraproduct operators from the product of Hardy spaces H p(X) × H q(X) to the Hardy space H r(X),where p,q,r ∈(n/(n + 1),∞) satisfy 1/p + 1/q = 1/r.Certain endpoint estimates are also obtained.In view of the lack of the Fourier transform in this setting,the proofs are based on the derivation of appropriate kernel estimates. | GRAFAKOS Loukas | 2010 | Science China Mathematics2010，53，8： | 7 |
| 3 | Some remarks on multilinear maps and interpolation显示文摘 | Loukas Grafakos Nigel Kalton | 2001 | Mathematische Annalen2001，，1： | 1 |
| 4 | Compensated compactness and the Heisenberg group显示文摘 | Loukas Grafakos Richard Rochberg | 1995 | Mathematische Annalen1995，，1： | 1 |
| 5 | Multilinear Calderon-Zygmund theory显示文摘 | LOUKAS Grafakos TORRES R | 2002 | Adv in Maths2002，165，1： | 1 |
| 6 | On multilinear singular integrals of Caldeon-Zygmund type显示文摘 | LOUKAS Grafakos TORRES R | 2002 | Publ Mat2002，，： | 1 |
| 7 | Best constants for two nonconvolution inequalities显示文摘 | Michael Christ Loukas Grafakos | 1995 | Proceedings of the American Mathematical Society1995，，6： | 1 |
| 8 | RD-空间上Hardy空间的极大函数特征及其应用显示文摘令X为RD-空间,即Coifman和Weiss意义下的齐型空间且满足逆双倍条件.设X具有'维数'n.对α∈(0,∞),分别记H^p_α(X),H^p_d(X)和H^(*,p)(X)为X上相应于非切向极大函数,二进极大函数和主极大函数的Hardy空间.利用一个新建立的Calderón再生公式,证明了当p∈(1,∞]时这些Hardy空间等价于L^p(X)及当p∈(n/(n+1),1]时这些Hardy空间彼此等价.对p∈(n/(n+1),1],建立了H^(*,p)(X)的原子特征刻画;进一步,当p∈(n/(n+1),1]时,证明了H^(*,p)(X)与Coifman和Weiss意义下的原子Hardy空间等价.此外,证明了一个次线性算子T可以唯一延拓为H^p(X)到某拟Banach空间B的有界算子当且仅当T将所有的(p,q)-原子,q∈(p,∞)∩[1,∞),或者连续的(p,∞)-原子映为B中的一致有界集. | Loukas GRAFAKOS 刘丽光 杨大春 | 2008 | 中国科学(A辑)2008，38，5： | 1 |
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