In this paper.the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces,weak Hardy spaces and Herz-type Hardy sp...In this paper.the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces,weak Hardy spaces and Herz-type Hardy spaces.展开更多
We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method,...We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.展开更多
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 H α p (X), H d p (X...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 H α p (X), H d p (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 Calderón reproducing formula, it is shown that all these Hardy spaces coincide with L p (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 H p (X) defined via the Littlewood-Paley function, and the atomic Hardy space of Coifman andWeiss coincide. Furthermore, it is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from H p (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.展开更多
基金supported by NSF of China(Grant:19971010)DPFIHE of China(Grant:98002703)National 973 Project of China
文摘In this paper.the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces,weak Hardy spaces and Herz-type Hardy spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.11471042,11171027 and 11361020)the Alexander von Humboldt Foundation+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2013YB60 and 2014KJJCA10)
文摘We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.
基金supported by the National Science Foundation of USA (Grant No. DMS 0400387)the University of Missouri Research Council (Grant No. URC-07-067)+1 种基金the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425106)the Program for New Century Excellent Talents in University of the Ministry of Education of China (Grant No. 04-0142)
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 H α p (X), H d p (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 Calderón reproducing formula, it is shown that all these Hardy spaces coincide with L p (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 H p (X) defined via the Littlewood-Paley function, and the atomic Hardy space of Coifman andWeiss coincide. Furthermore, it is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from H p (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.
