In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted esti...In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator展开更多
Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the...Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.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
基金This research was supported by the NSFC （10971228）.
文摘In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator
基金NNSF(No.10271015)of ChinaRFDP(No.20020027004)of China
文摘Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.
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.
