Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neum...Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.展开更多
Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where ...Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.展开更多
We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Trieb...For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.展开更多
In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ （0, ∞...In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ （0, ∞） with 1/p = ∑k=1^m 1/pk, then for any weight w, integer l with 1 〈 e 〈 m,展开更多
Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） t...Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） to the weighted weak Hardy spaces WHwp （Rn） for 0 〈 p 〈 1 and δ = n/p- （n ＋ 1）/2. This result is new even in the unweighted case.展开更多
Abstract. The authors introduce the (θ1,θ2)-type Calderon-Zygmund operators andthe operators with the semi-(θ, N) regular kernels, and study their boundedness on theweighted Lebesgue spacest the weighted weak Lebes...Abstract. The authors introduce the (θ1,θ2)-type Calderon-Zygmund operators andthe operators with the semi-(θ, N) regular kernels, and study their boundedness on theweighted Lebesgue spacest the weighted weak Lebesgue spaces, the weighted Hardy spacesand the weighted weak Hardy spaces.展开更多
To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is boun...To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the halfplane for all index choices.For applications,we obtain direct analytic characterizations of the bounded and compact differences of composition operators on such spaces.This paper concludes with a joint Carleson measure characterization when the difference of composition operators is Hilbert-Schmidt.展开更多
In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.
We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decompositio...We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.展开更多
In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the e...In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.展开更多
文摘Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171027, 11101339） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20120003110003）.
文摘Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.
文摘The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.
基金Sponsored by the NSF of South-Central University for Nationalities (YZZ08004)the Doctoral programme foundation of National Education Ministry of China
文摘For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.
文摘In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ （0, ∞） with 1/p = ∑k=1^m 1/pk, then for any weight w, integer l with 1 〈 e 〈 m,
文摘Let w be a Muckenhoupt weight and Hwp （JRn） be the weighted Hardy space. In this paper, by using the atomic decomposition of Hwp（Rn）, we will show that the Bochner-Riesz operators TRδ are bounded from Hwp（Rn） to the weighted weak Hardy spaces WHwp （Rn） for 0 〈 p 〈 1 and δ = n/p- （n ＋ 1）/2. This result is new even in the unweighted case.
文摘Abstract. The authors introduce the (θ1,θ2)-type Calderon-Zygmund operators andthe operators with the semi-(θ, N) regular kernels, and study their boundedness on theweighted Lebesgue spacest the weighted weak Lebesgue spaces, the weighted Hardy spacesand the weighted weak Hardy spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.11771340 and 11431011)。
文摘To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the halfplane for all index choices.For applications,we obtain direct analytic characterizations of the bounded and compact differences of composition operators on such spaces.This paper concludes with a joint Carleson measure characterization when the difference of composition operators is Hilbert-Schmidt.
文摘In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.
基金supported by National Natural Science Foundation of China(Grant No.10971228)supported by National Natural Science Foundation of China(Grant No.11071200)
文摘In this paper, the authors establish the boundedness of the multilinear Calderon-Zygmund operator from products of Hardy spaces into Hardy spaces
基金supported in part by the National Natural Science Foundation of China(Grant No.11761026,11761027)Natural Science Foundation of Guangxi(Grant No.2020GXNSFAA159085).
文摘We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.
基金Supported by the Xinjiang Training of Innovative Personnel Natural Science Foundation of China(Grant No.2020D01C048)the National Natural Science Foundation of China(Grant No.11861062)。
文摘In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.
