Let A be an expansive dilation. We define weakly strongly singular integral kernels and study the action of the operators induced by these kernels on anisotropic Hardy spaces associated with A.
Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.
In this paper we give the conditions on the pair （~1, W2） which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized Morrey space Mp,w1 to anot...In this paper we give the conditions on the pair （~1, W2） which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized Morrey space Mp,w1 to another Mp,w2, 1 〈 p 〈 ∞, and from the space M1,w1 to the weak space M1,w2.展开更多
In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ<SUP> n </SUP>are introduced, and the central atomic and molecular decomposition characte...In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ<SUP> n </SUP>are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces.展开更多
In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also...In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.展开更多
Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish...Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A.展开更多
Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz ...Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.展开更多
We consider the boundedness of Calderón-Zygmund operators from Hp,}(R^n)(the predual of a Morrey space) to h^p,}(R^n)(the local version of H^p,}). We show that Calderón's commutator is bounded from H^p,}...We consider the boundedness of Calderón-Zygmund operators from Hp,}(R^n)(the predual of a Morrey space) to h^p,}(R^n)(the local version of H^p,}). We show that Calderón's commutator is bounded from H^p,} to h^p,}.展开更多
In this paper, two classes of closely related multilinear singular andfractional integrals, which include the commutators as special cases, are studied and theirboundedness on Herz type spaces is discussed. In fact, i...In this paper, two classes of closely related multilinear singular andfractional integrals, which include the commutators as special cases, are studied and theirboundedness on Herz type spaces is discussed. In fact, it is proved that these operators areactually not bounded in certain extreme cases.展开更多
基金supported by NSF of China (Grant No.10571015)RFDP of China (Grant No.20050027025)NSF of Zhejiang Province (Grant No.Y7080325)
文摘Let A be an expansive dilation. We define weakly strongly singular integral kernels and study the action of the operators induced by these kernels on anisotropic Hardy spaces associated with A.
基金NNSFC(11771223,11501308)Natural science foundation of Inner Mongolia(2019MS01003).
文摘Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's identity.As an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.
文摘In this paper we give the conditions on the pair （~1, W2） which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized Morrey space Mp,w1 to another Mp,w2, 1 〈 p 〈 ∞, and from the space M1,w1 to the weak space M1,w2.
基金NSF of China (Grant Nos.10571014 and 10571015)SRFDP of China (Grant No.20050027025)
文摘In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ<SUP> n </SUP>are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces.
基金supported by the National Natural Science Foundation of China (Grant No. 10571015)Specialized Research Foundation for Doctor Programme (Grant No. 20050027025)
文摘In this paper, the authors establish the anisotropic weak Hardy spaces associated with very general discrete groups of dilations. Moreover, the atomic decomposition theorem of the anisotropic weak Hardy spaces is also given. As some applications of the above results, the authors prove some interpolation theorems and obtain the boundedness of the singular integral operators on these Hardy spaces.
基金supported by National Natural Science Foundation of China (Grant Nos. 11571039, 11361020 and 11471042)
文摘Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671414, 11271091, 11471040, 11461065, 11661075, 11571039 and 11671185)
文摘Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.
文摘We consider the boundedness of Calderón-Zygmund operators from Hp,}(R^n)(the predual of a Morrey space) to h^p,}(R^n)(the local version of H^p,}). We show that Calderón's commutator is bounded from H^p,} to h^p,}.
基金This project is supported by the RFDP(No.20020027004)NNSF(No.10271015)of China
文摘In this paper, two classes of closely related multilinear singular andfractional integrals, which include the commutators as special cases, are studied and theirboundedness on Herz type spaces is discussed. In fact, it is proved that these operators areactually not bounded in certain extreme cases.
