In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermor...In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermore,norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces.展开更多
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Lit...In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.展开更多
In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are...In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.展开更多
The Ba space was introduced and studied at first in [1]. It has been effectively applied to the prior estimates for linear partial differential equations, to the calculus of variations with strong nonlinearity, to the...The Ba space was introduced and studied at first in [1]. It has been effectively applied to the prior estimates for linear partial differential equations, to the calculus of variations with strong nonlinearity, to the error estimations for finite difference methods and to harmonic analysis (cf.[1--8] ). The goal of this report is to study the Littlewood-Paley theory in the Ba spaces.展开更多
Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Litt...Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.展开更多
Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Little...Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function,we obtain several equivalent characterizations of Hp(·)(Rn) in terms of wavelets,which extend the wavelet characterizations of the classical Hardy spaces.The main ingredients are that,we overcome the difficulties of the quasi-norms of Hp(·)(Rn) by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on Lp(·)(Rn),and also overcome the difficulty of the failure of q =2 in the atomic decomposition of Hp(·) (Rn) by a known idea.展开更多
基金Supported in part by the Natural Science Foundation of China(11471309 and 11561062)。
文摘In this paper,we consider the boundedness of multilinear Littlewood-Paley operators which include multilinear g-function,multilinear Lusin's area integral and multilinear Littlewood-Paley g^*λ-function.Furthermore,norm inequalities of the above operators hold on the corresponding Amalgam-Campanato spaces.
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
基金The Excellent Young Talent Foundation(2013SQRL080ZD)of Anhui Province
文摘In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.
文摘In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.
文摘The Ba space was introduced and studied at first in [1]. It has been effectively applied to the prior estimates for linear partial differential equations, to the calculus of variations with strong nonlinearity, to the error estimations for finite difference methods and to harmonic analysis (cf.[1--8] ). The goal of this report is to study the Littlewood-Paley theory in the Ba spaces.
基金Supported by National Natural Science Foundation of China(Grant No.11471040)the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)
文摘Let （x, d,u） be a metric measure the upper doubling conditions. Under the weak space satisfying both the geometrically doubling and reverse doubling condition, the authors prove that the generalized homogeneous Littlewood-Paley g-function gr （r ∈ [2, ∞）） is bounded from Hardy space H1（u） into L1（u）. Moreover, the authors show that, if f ∈ RBMO（u）, then [gr（f）]r is either infinite everywhere or finite almost everywhere, and in the latter case, [gr（f）]r belongs to RBLO（u） with the norm no more than ｜｜f｜｜ RBMO（u） multiplied by a positive constant which is independent of f. As a corollary, the authors obtain the boundedness of gr from RBMO（u） into RBLO（u）. The vector valued Calderon-Zygmund theory over （X, d, u） is also established with details in this paper.
基金The author would like to express his deep thanks to the anonymous referees for their several enlightening comments on this article, which do improve the presen tat ion of this article. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11701160, 11871100).
文摘Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent,Hp(·)(Rn),into Lebesgue spaces with variable exponent,Lp(·) (Rn),and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function,we obtain several equivalent characterizations of Hp(·)(Rn) in terms of wavelets,which extend the wavelet characterizations of the classical Hardy spaces.The main ingredients are that,we overcome the difficulties of the quasi-norms of Hp(·)(Rn) by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on Lp(·)(Rn),and also overcome the difficulty of the failure of q =2 in the atomic decomposition of Hp(·) (Rn) by a known idea.
