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| 1 | Local Hardy spaces of Musielak-Orlicz type and their applications显示文摘Letφ:R n × [0,∞) → [0,∞) be a function such that φ(x,·) is an Orlicz function and (·,t) ∈ A ∞loc (Rn) (the class of local weights introduced by Rychkov).In this paper,the authors introduce a local Musielak-Orlicz Hardy space hφ(Rn) by the local grand maximal function,and a local BMO-type space bmoφ(Rn) which is further proved to be the dual space of hφ(Rn).As an application,the authors prove that the class of pointwise multipliers for the local BMO-type space bmo φ (Rn),characterized by Nakai and Yabuta,is just the dual of L 1 (Rn) + h Φ 0 (Rn),where φ is an increasing function on (0,∞) satisfying some additional growth conditions and Φ 0 a Musielak-Orlicz function induced by φ.Characterizations of hφ(Rn),including the atoms,the local vertical and the local nontangential maximal functions,are presented.Using the atomic characterization,the authors prove the existence of finite atomic decompositions achieving the norm in some dense subspaces of hφ(Rn),from which,the authors further deduce some criterions for the boundedness on hφ(Rn) of some sublinear operators.Finally,the authors show that the local Riesz transforms and some pseudo-differential operators are bounded on hφ(Rn). | YANG DaChun YANG SiBei | 2012 | Science China Mathematics2012，55，8： | 13 |
| 2 | Applications of Orlicz-Hardy spaces associated with operators satisfying Poisson estimates显示文摘Let L be a linear operator in L2 (Rn) and generate an analytic semigroup {e-tL } t 0 with kernel satisfying an upper bound estimate of Poisson type,whose decay is measured by θ(L) ∈ (0,∞).Let Φ be a positive,continuous and strictly increasing function on (0,∞),which is of strictly critical lower type p Φ∈ (n/(n + θ(L)),1].Denote by H Φ,L (Rn) the Orlicz-Hardy space introduced in Jiang,Yang and Zhou's paper in 2009.If Φ is additionally of upper type 1 and subadditive,the authors then show that the Littlewood-Paley g-function g L maps H Φ,L (Rn) continuously into L Φ (Rn) and,moreover,the authors characterize H Φ,L (Rn) in terms of the Littlewood-Paley g λ-function with λ∈ (n(2/p Φ + 1),∞).If Φ is further slightly strengthened to be concave,the authors show that a generalized Riesz transform associated with L is bounded from H Φ,L (Rn) to the Orlicz space L Φ (Rn) or the Orlicz-Hardy space H Φ (Rn);moreover,the authors establish a new subtle molecular characterization of H Φ,L (Rn) associated with L and,as applications,the authors then show that the corresponding fractional integral L-γ for certain γ∈ (0,∞) maps H Φ,L (Rn) continuously into H Φ,L (Rn),where Φ satisfies the same properties as Φ and is determined by Φ and γ,and also that L has a bounded holomorphic functional calculus in H Φ,L (Rn).All these results are new even when Φ(t) ≡ tp for all t ∈ (0,∞) and p ∈ (n/(n + θ(L)),1]. | LIANG YiYu YANG DaChun YANG SiBei | 2011 | Science China Mathematics2011，54，11： | 11 |
| 3 | Decompositions of non-homogeneous Herz-type Besov and Triebel-Lizorkin spaces显示文摘Decompositions of non-homogeneous Herz-type Besov and Triebel-Lizorkin spaces by atoms,molecules and wavelets are given.These results generalize the corresponding results for classical Besov and Triebel-Lizorkin spaces. | XU JingShi | 2014 | Science China Mathematics2014，57，2： | 3 |
| 4 | Multiple weighted estimates for commutators of multilinear fractional integral operators显示文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011. | CHEN SongQing WU HuoXiong | 2013 | Science China Mathematics2013，56，9： | 2 |
| 5 | THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERóN-ZYGMUND OPERATORS显示文摘Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMOw(R^n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R^n,A)),the commutator[b,T]is bounded from anisotropic weighted Hardy space H^1ω(R^n,A)to weighted Lebesgue space L^1ω(R^n)and when b∈BMO(R^n)(bounded mean oscillation space),the commutator[b,T]is bounded on Musielak-Orlicz space L^φ(R^n),which are extensions of the isotropic setting. | 李金霞 李宝德 何建勋 | 2020 | Acta Mathematica Scientia2020，40，1： | 1 |
| 6 | 与广义Schrodinger算子相关的Herz型Hardy空间显示文摘假设L=-Δ+μ是R^n(n≥3)上的广义Schr?dinger算子,其中μ■0是非负Radon测度满足尺度不变的Kato条件和双倍条件.本文引进了与广义Schr?dinger算子L相关的Herz型Hardy空间,证明了与广义Schr?dinger算子L相关的Herz型Hardy空间的原子分解,作为应用,得到了与广义Schr?dinger算子L相关的Marcinkiewicz积分μ_j^L在Herz型Hardy空间上的有界性. | 韩瑶瑶 赵凯 | 2020 | 数学进展2020，49，5： | 1 |
| 7 | 与算子相连的面积积分在乘积空间中的有界性显示文摘本文假设自伴算子L_(1)与L_(2)的热半群满足非对角估计(GGE_(p0)),其中p_(0)∈[1,2).在乘积空间R^(n_(1))×R^(n_(2))中,本文通过自伴算子L_(1)与L_(2)的热半群定义了与算子相连的面积积分S,证明了当p∈(p0,p’0)时,面积积分S在L^(p)(R^(n_(1))×R^(n_(2)))中的有界性. | 宋娟 邓清泉 | 2024 | 中国科学:数学2024，54，1： | 0 |
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