The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several cl... The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.展开更多
In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is...In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is merely assumed on a size condition.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the produc...The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderon-Zygmund operators and multilinear fractional integral operators can be deduced, resDectivelv.展开更多
We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn...We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn） =μ^-∑i=1^n α≥1 k（x, ξ）, αi≥ 1 and μ 〉 0. The continuity of this operator in L^（^＇＇） is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces L^p,ω（R^n）, p ∈ （1, ∞） with a weight w satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator C[α, k]=Kα- αK with the operator of multiplication by BMO functions.展开更多
Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded...Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.展开更多
Let L be a linear operator in L 2 (? n ) and generate an analytic semigroup {e ?tL }t?0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper ...Let L be a linear operator in L 2 (? n ) and generate an analytic semigroup {e ?tL }t?0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper type 1 and of critical lower type p o (ω) ? (n/(n+θ(L)),1] and ρ(t) = t t1/ω ?1(t ?1) for t ∈ (0,∞). We introduce the Orlicz-Hardy space H ω, L (? n ) and the BMO-type space BMO ρ, L (? n ) and establish the John-Nirenberg inequality for BMO ρ, L (? n ) functions and the duality relation between H ω, L ((? n ) and BMO ρ, L* (? n ), where L* denotes the adjoint operator of L in L 2 (? n ). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMO ρ, L* (? n ) and the molecular characterization of H ω, L (? n ); the latter is used to establish the boundedness of the generalized fractional operator L ρ ?γ from H ω, L (? n ) to H L 1 (? n ) or L q (? n ) with certain q > 1, where H L (? n ) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = t p for t ∈ (0,∞) and p ∈ (n/(n + θ(L)), 1].展开更多
In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution...In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.展开更多
In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and Lipschitz function b∈Λβ0(Rn) is discussed from Lp(Rn) to Lq(Rn), 1/q=1/p-β0/n, and from Lp(Rn) ...In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and Lipschitz function b∈Λβ0(Rn) is discussed from Lp(Rn) to Lq(Rn), 1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space Fβ0,∞p. We also obtain the boundedness of generalized Toeplitz operatorθbα0 from LP(Rn) to Lq(Rn), 1/q =1/p-α0+β0/n. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and BMO function b is discussed on LP(Rn), 1 < p <∞.展开更多
It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of s...It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.展开更多
In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 【 p 【 ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and exte...In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 【 p 【 ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and extension of some known results.展开更多
In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdl...In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdlya operators） and the central BMO functions are bounded on L^q （｜x｜apdx）, more generally, on Herz spaces.展开更多
文摘 The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.
基金This research is supported by the NNSF (Grant:19971010)National 973 Project of China.
文摘In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is merely assumed on a size condition.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
基金National Natural Science Foundation of China (10571014)the Doctoral Programme Foundation of Institution of Higher Education of China (20040027001)
文摘The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderon-Zygmund operators and multilinear fractional integral operators can be deduced, resDectivelv.
文摘We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn） =μ^-∑i=1^n α≥1 k（x, ξ）, αi≥ 1 and μ 〉 0. The continuity of this operator in L^（^＇＇） is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces L^p,ω（R^n）, p ∈ （1, ∞） with a weight w satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator C[α, k]=Kα- αK with the operator of multiplication by BMO functions.
文摘Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.
基金supported by National Science Foundation for Distinguished Young Scholars of China (GrantNo. 10425106)
文摘Let L be a linear operator in L 2 (? n ) and generate an analytic semigroup {e ?tL }t?0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper type 1 and of critical lower type p o (ω) ? (n/(n+θ(L)),1] and ρ(t) = t t1/ω ?1(t ?1) for t ∈ (0,∞). We introduce the Orlicz-Hardy space H ω, L (? n ) and the BMO-type space BMO ρ, L (? n ) and establish the John-Nirenberg inequality for BMO ρ, L (? n ) functions and the duality relation between H ω, L ((? n ) and BMO ρ, L* (? n ), where L* denotes the adjoint operator of L in L 2 (? n ). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMO ρ, L* (? n ) and the molecular characterization of H ω, L (? n ); the latter is used to establish the boundedness of the generalized fractional operator L ρ ?γ from H ω, L (? n ) to H L 1 (? n ) or L q (? n ) with certain q > 1, where H L (? n ) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = t p for t ∈ (0,∞) and p ∈ (n/(n + θ(L)), 1].
基金Supported by the National Natural Science Foundation of China （No.10571016） and Science Foundation for the Excellent Young Teacher of Henan Province.
文摘In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.
基金The This work was supported by the National Natural Science Foundation of China(Grant No.10571014)the Doctoral Programme Foundation of Institution of Higher Education of China(Grant No.20040027001).
文摘In this paper, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and Lipschitz function b∈Λβ0(Rn) is discussed from Lp(Rn) to Lq(Rn), 1/q=1/p-β0/n, and from Lp(Rn) to Triebel-Lizorkin space Fβ0,∞p. We also obtain the boundedness of generalized Toeplitz operatorθbα0 from LP(Rn) to Lq(Rn), 1/q =1/p-α0+β0/n. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator Tb(f) related to strongly singular Calderon-Zygmund operators and BMO function b is discussed on LP(Rn), 1 < p <∞.
基金Supported by National Natural Science Foundation of China （Grant No. 11071250） NWNU-KJCXGC-3-47 The authors would like to express their deep thanks to the referee for his/her very careful reading and many valuable comments and suggestions
文摘In this paper, the authors give the boundedness on Triebel-Lizorkin spaces for the parabolic singular integral with rough kernel and its commutator.
文摘It is well known that the commutator Tb of the singular integral operator T with a BMO function b is bounded on L^P（R^n）, 1 〈 p 〈 ∞. In this paper, we consider the endpoint estimates for a kind of commutator of singular integrals. A BMO-type estimate for Tb is obtained under the assumption b ∈ LMO.
基金supported by National Natural Science Foundation of China (GrantNos. 10871024, 10901076)Natural Science Foundation of Shandong Province (Grant No. Q2008A01)+1 种基金supported by National Natural Science Foundation of China (Grant Nos. 10871024, 10931001)supported by the Key Laboratory of Mathematics and Complex System (Beijing Normal University), Ministry of Education,China
文摘In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
基金supported by National Natural Science Foundation of China (Grant Nos.10931001,10901017)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090003110018)Natural Science Foundation of Zhejiang Province (Grant No.Y7080325)
文摘In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 【 p 【 ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and extension of some known results.
基金Supported by National Natural Science Foundation of China(Grant Nos.10901076,10931001,11126203and11171345)Natural Science Foundation of Shandong Province(Grant No.ZR2010AL006)
文摘In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdlya operators） and the central BMO functions are bounded on L^q （｜x｜apdx）, more generally, on Herz spaces.
