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
Let L be a linear operator in L2 (Rn) and generate an analytic semigroup {e-tL } t 0 with kernel satisfying an upper bound estimate of Poisson type,whose decay is measured by θ(L) ∈ (0,∞).Let Φ be a positive,conti...Let L be a linear operator in L2 (Rn) and generate an analytic semigroup {e-tL } t 0 with kernel satisfying an upper bound estimate of Poisson type,whose decay is measured by θ(L) ∈ (0,∞).Let Φ be a positive,continuous and strictly increasing function on (0,∞),which is of strictly critical lower type p Φ∈ (n/(n + θ(L)),1].Denote by H Φ,L (Rn) the Orlicz-Hardy space introduced in Jiang,Yang and Zhou's paper in 2009.If Φ is additionally of upper type 1 and subadditive,the authors then show that the Littlewood-Paley g-function g L maps H Φ,L (Rn) continuously into L Φ (Rn) and,moreover,the authors characterize H Φ,L (Rn) in terms of the Littlewood-Paley g λ-function with λ∈ (n(2/p Φ + 1),∞).If Φ is further slightly strengthened to be concave,the authors show that a generalized Riesz transform associated with L is bounded from H Φ,L (Rn) to the Orlicz space L Φ (Rn) or the Orlicz-Hardy space H Φ (Rn);moreover,the authors establish a new subtle molecular characterization of H Φ,L (Rn) associated with L and,as applications,the authors then show that the corresponding fractional integral L-γ for certain γ∈ (0,∞) maps H Φ,L (Rn) continuously into H Φ,L (Rn),where Φ satisfies the same properties as Φ and is determined by Φ and γ,and also that L has a bounded holomorphic functional calculus in H Φ,L (Rn).All these results are new even when Φ(t) ≡ tp for all t ∈ (0,∞) and p ∈ (n/(n + θ(L)),1].展开更多
In this paper,the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fp,q s,w(Rn)with local weight w by using the Lusin-area functions for the full ranges of the indices,and then establish their atomic dec...In this paper,the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fp,q s,w(Rn)with local weight w by using the Lusin-area functions for the full ranges of the indices,and then establish their atomic decompositions for s ∈ R,p ∈(0,1] and q ∈ [p,∞).The novelty is that the weight w here satisfies the classical Muckenhoupt condition only on balls with their radii in(0,1].Finite atomic decompositions for smooth functions in Fp,q s,w(Rn)are also obtained,which further implies that a(sub)linear operator that maps smooth atoms of Fp,q s,w(Rn)uniformly into a bounded set of a(quasi-)Banach space is extended to a bounded operator on the whole Fp,q s,w(Rn).As an application,the boundedness of the local Riesz operator on the space Fp,q s,w(Rn)is obtained.展开更多
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.
基金supported by National Natural Science Foundation of China (Grant No. 10871025)Program for Changjiang Scholars and Innovative Research Team in Universities of China
文摘Let L be a linear operator in L2 (Rn) and generate an analytic semigroup {e-tL } t 0 with kernel satisfying an upper bound estimate of Poisson type,whose decay is measured by θ(L) ∈ (0,∞).Let Φ be a positive,continuous and strictly increasing function on (0,∞),which is of strictly critical lower type p Φ∈ (n/(n + θ(L)),1].Denote by H Φ,L (Rn) the Orlicz-Hardy space introduced in Jiang,Yang and Zhou's paper in 2009.If Φ is additionally of upper type 1 and subadditive,the authors then show that the Littlewood-Paley g-function g L maps H Φ,L (Rn) continuously into L Φ (Rn) and,moreover,the authors characterize H Φ,L (Rn) in terms of the Littlewood-Paley g λ-function with λ∈ (n(2/p Φ + 1),∞).If Φ is further slightly strengthened to be concave,the authors show that a generalized Riesz transform associated with L is bounded from H Φ,L (Rn) to the Orlicz space L Φ (Rn) or the Orlicz-Hardy space H Φ (Rn);moreover,the authors establish a new subtle molecular characterization of H Φ,L (Rn) associated with L and,as applications,the authors then show that the corresponding fractional integral L-γ for certain γ∈ (0,∞) maps H Φ,L (Rn) continuously into H Φ,L (Rn),where Φ satisfies the same properties as Φ and is determined by Φ and γ,and also that L has a bounded holomorphic functional calculus in H Φ,L (Rn).All these results are new even when Φ(t) ≡ tp for all t ∈ (0,∞) and p ∈ (n/(n + θ(L)),1].
基金supported by the National Natural Science Foundation of China(Nos.11101425,11171027)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20120003110003)
文摘In this paper,the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fp,q s,w(Rn)with local weight w by using the Lusin-area functions for the full ranges of the indices,and then establish their atomic decompositions for s ∈ R,p ∈(0,1] and q ∈ [p,∞).The novelty is that the weight w here satisfies the classical Muckenhoupt condition only on balls with their radii in(0,1].Finite atomic decompositions for smooth functions in Fp,q s,w(Rn)are also obtained,which further implies that a(sub)linear operator that maps smooth atoms of Fp,q s,w(Rn)uniformly into a bounded set of a(quasi-)Banach space is extended to a bounded operator on the whole Fp,q s,w(Rn).As an application,the boundedness of the local Riesz operator on the space Fp,q s,w(Rn)is obtained.
