The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space....The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.展开更多
Let φ be a growth function, and let A ：= -（V- ia）. （V- ia）＋ V be a magnetic SchrSdinger operator on L2（Rn）, n≥ 2, where a ：= （a1, a2... an） ∈ r L1 loc（Rn） We establish the equivalent characteriza- L2 ...Let φ be a growth function, and let A ：= -（V- ia）. （V- ia）＋ V be a magnetic SchrSdinger operator on L2（Rn）, n≥ 2, where a ：= （a1, a2... an） ∈ r L1 loc（Rn） We establish the equivalent characteriza- L2 1oc（Rn, Rn） and 0 ≤ V ∈Lloc（Rn） tions of the Musielak-Orlicz-Hardy space HA,^（IRn）, defined by the Lusin area function associated with {e-t2A}t〉0, in terms of the Lusin area function associated with {e-t√A}t〉0, the radial maximal functions and the non- tangential maximal functions associated with {e-t2A}t〉o and {e-t√A}t〉0, respectively. The boundedness of the Riesz transforms LkA-U1/2, k ∈ {1, 2... n}, from HA,φ（Rn） to Lφ（Rn） is also presented, where Lk is the closure of δ/δxk iak in L2（Rn）. These results are new even when φ（x,t） ：= w（x）tp for all x ∈Rn and t∈ （0, ＋∞） with p ∈ （0, 1] and ω∈ A∞（Rn） （the class of Muckenhoupt weights on Rn）.展开更多
In this article,we introduce the martingale Musielak-Orlicz Hardy spaces H_φ^*(■),Pφ(?),H_φ^S(■),Qφ(?)and H_φ^s(■),respectively,via the maximal function,the quadratic variation and the conditional quadratic va...In this article,we introduce the martingale Musielak-Orlicz Hardy spaces H_φ^*(■),Pφ(?),H_φ^S(■),Qφ(?)and H_φ^s(■),respectively,via the maximal function,the quadratic variation and the conditional quadratic variation of martingales.We then establish the atomic characterizations of H_φ^s(■),Pφ(■)and Qφ(■).As applications,we obtain the dual space of H_φ^s(■)and several martingale inequalities which further clarify the relations among H_φ^*(■),Pφ(■),H_φ^S(■),Qφ(■)and H_φ^s(■).Especially,as special cases,the results on atomic characterizations of H_φ^s(■),Pφ(?)and Qφ(■)as well as on the dual space of H_φ^s(■)in the weighted case are also new.展开更多
Anisotropy is a common attribute of the nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathemat...Anisotropy is a common attribute of the nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics,can be expressed by a fairly general discrete group of dilations where A is a real matrix with all its elgenvalues A satisfy . The aim of this article is to study a general class of anisotropic function spaces, some properties and applications of these spaces. Let be an anisotropic p-growth function with . The purpose of this article is to find an appropriate general space which includes weak Hardy space of Fefferman and Soria, weighted weak Hardy space of Quek and Yang, and anisotropic weak Hardy space of Ding and Lan. For this reason, we introduce the anisotropic weak Hardy space of Musielak-Orlicz type and obtain its atomic characterization. As applications, we further obtain an interpolation theorem adapted to and the boundedness of the anisotropic Calder6n-Zygmund operator from. It is worth mentioning that the superposition principle adapted to the weak Musielak-Orlicz function space, which is an extension of a result of E. M. Stein, M. Taibleson and G. Weiss, plays an important role in the proofs of the atomic decomposition of and the interpolation theorem.展开更多
文摘The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.
基金supported by the National Natural Science Foundation of China(11461065)Scientific Research Projects in Colleges and Universities in Xinjiang Uyghur Autonomous Region(XJEDU2014S001)
文摘Let φ be a growth function, and let A ：= -（V- ia）. （V- ia）＋ V be a magnetic SchrSdinger operator on L2（Rn）, n≥ 2, where a ：= （a1, a2... an） ∈ r L1 loc（Rn） We establish the equivalent characteriza- L2 1oc（Rn, Rn） and 0 ≤ V ∈Lloc（Rn） tions of the Musielak-Orlicz-Hardy space HA,^（IRn）, defined by the Lusin area function associated with {e-t2A}t〉0, in terms of the Lusin area function associated with {e-t√A}t〉0, the radial maximal functions and the non- tangential maximal functions associated with {e-t2A}t〉o and {e-t√A}t〉0, respectively. The boundedness of the Riesz transforms LkA-U1/2, k ∈ {1, 2... n}, from HA,φ（Rn） to Lφ（Rn） is also presented, where Lk is the closure of δ/δxk iak in L2（Rn）. These results are new even when φ（x,t） ：= w（x）tp for all x ∈Rn and t∈ （0, ＋∞） with p ∈ （0, 1] and ω∈ A∞（Rn） （the class of Muckenhoupt weights on Rn）.
基金supported by National Natural Science Foundation of China (Grant Nos. 11471337, 11722114, 11571039 and 11671185)
文摘In this article,we introduce the martingale Musielak-Orlicz Hardy spaces H_φ^*(■),Pφ(?),H_φ^S(■),Qφ(?)and H_φ^s(■),respectively,via the maximal function,the quadratic variation and the conditional quadratic variation of martingales.We then establish the atomic characterizations of H_φ^s(■),Pφ(■)and Qφ(■).As applications,we obtain the dual space of H_φ^s(■)and several martingale inequalities which further clarify the relations among H_φ^*(■),Pφ(■),H_φ^S(■),Qφ(■)and H_φ^s(■).Especially,as special cases,the results on atomic characterizations of H_φ^s(■),Pφ(?)and Qφ(■)as well as on the dual space of H_φ^s(■)in the weighted case are also new.
文摘Anisotropy is a common attribute of the nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics,can be expressed by a fairly general discrete group of dilations where A is a real matrix with all its elgenvalues A satisfy . The aim of this article is to study a general class of anisotropic function spaces, some properties and applications of these spaces. Let be an anisotropic p-growth function with . The purpose of this article is to find an appropriate general space which includes weak Hardy space of Fefferman and Soria, weighted weak Hardy space of Quek and Yang, and anisotropic weak Hardy space of Ding and Lan. For this reason, we introduce the anisotropic weak Hardy space of Musielak-Orlicz type and obtain its atomic characterization. As applications, we further obtain an interpolation theorem adapted to and the boundedness of the anisotropic Calder6n-Zygmund operator from. It is worth mentioning that the superposition principle adapted to the weak Musielak-Orlicz function space, which is an extension of a result of E. M. Stein, M. Taibleson and G. Weiss, plays an important role in the proofs of the atomic decomposition of and the interpolation theorem.
