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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 | Multilinear Calderón-Zygmund theory显示文摘 | Grafakos L Tones R H | 2002 | Advances in Mathematics2002，165，1： | 1 |
| 4 | Best constants for two nonconvolution inequalities显示文摘 | Christ M Grafakos L | | 0，，： | 1 |
| 5 | Bilinear operators on Herz - type spacea显示文摘 | Grafakos L Li X Yang D | 1998 | Trans Amer Math Soc1998，，： | 1 |
| 6 | Multilinear Calder6n-Zygmund the- ory显示文摘 | Grafakos L Torres R | 2002 | Adv Math2002，165，1： | 1 |
| 7 | Maximal operator and weighted norm inequalities for multilinear singular integrals 显示文摘 | Grafakos L Torres R | 2002 | In- diana U Math J2002，51，： | 1 |
| 8 | Bounds for singular integrals and maximal singular integrals with rough kemels显示文摘 | Grafakos L Stefanov A | 1998 | Indiana Univ Math J1998，47，： | 1 |
| 9 | Best constants for two nonconvolution inequalities显示文摘 | Christ M Grafakos L | 1995 | Proc Am Math Soc1995，123，： | 1 |
| 10 | On multilinear singular integrals of Caderón-Zygmund type显示文摘 | GRAFAKOS L TORRES R H | 2002 | Pub Math2002，，： | 1 |
| 11 | Discrete decompositions for bilinear operators and almost diagonal conditions显示文摘 | GRAFAKOS L TORRES R H | 2002 | Trans Amer Math Soc2002，354，： | 1 |
| 12 | Maximal operators and weighted norm inequalities for multilinear singular integrals显示文摘 | GRAFAKOS L TORRES R H | 2002 | Indiana Univ Math Journal2002，51，： | 1 |
| 13 | Some remarks on multilinear maps and interpolation显示文摘 | Loukas Grafakos Nigel Kalton | 2001 | Mathematische Annalen2001，，1： | 1 |
| 14 | Multilinear Calderón-Zygmund theory显示文摘 | GRAFAKOS L TORRES R H | 2002 | Adv in Math2002，165，1： | 1 |
| 15 | Maximal operators for multilinear singular integrals with non-smooth kernels显示文摘 | Duong X Gong R Grafakos L Li J Yan L | | 0，，： | 1 |
| 16 | Multilinear Calderon-Zygmud theory显示文摘 | Grafakos L Torres R | 2002 | Adv math2002，165，： | 1 |
| 17 | Multilinear operators with non-smooth kernels and commutators of singular integrals显示文摘 | Duong X Grafakos L Yan L | | 0，，： | 1 |
| 18 | On multilinear intergal of Calder6n-Zygmud type显示文摘 | Grafakos L Torres R | 2002 | Publ math2002，57，： | 1 |
| 19 | Maximal operator and weighted norm inequalities for multilinear singular integrals 显示文摘 | Grafakos L Torres R | 2002 | Indiana Univ Math J2002，51，5： | 1 |
| 20 | Multilinear Calder6n-Zygmund theory显示文摘 | Grafakos L Torres R H | | 0，，： | 1 |
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