The Bracket Set(dougong)is an important aspect of traditional Chinese architecture known for its exquisite structure,complexity,and rich variations.This design element has been used since the Qin and Han Dynasties and...The Bracket Set(dougong)is an important aspect of traditional Chinese architecture known for its exquisite structure,complexity,and rich variations.This design element has been used since the Qin and Han Dynasties and is still prevalent today.It highlights hierarchy and spiritual connotations in the design of a building.This article explores the application of Bracket Set elements in modern architectural design.It analyzes the specific application strategies of this design element,highlighting its value in modern architecture.The goal is to provide modern architectural designers with multiple perspectives and strategies to fully utilize the advantages of Bracket Set elements in architectural design and enhance the artistic value of their work.展开更多
In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The bo...In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).展开更多
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th...This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).展开更多
In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degr...In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).展开更多
文摘The Bracket Set(dougong)is an important aspect of traditional Chinese architecture known for its exquisite structure,complexity,and rich variations.This design element has been used since the Qin and Han Dynasties and is still prevalent today.It highlights hierarchy and spiritual connotations in the design of a building.This article explores the application of Bracket Set elements in modern architectural design.It analyzes the specific application strategies of this design element,highlighting its value in modern architecture.The goal is to provide modern architectural designers with multiple perspectives and strategies to fully utilize the advantages of Bracket Set elements in architectural design and enhance the artistic value of their work.
基金supported by the NNSF of China(12271483,11961056)the NSF of Jiangxi Province(20192BAB201004)+1 种基金supported by the“Xin-Miao”Program of Zhejiang Province(2021R415027)the Innovation Fund of ZUST(2020yjskc06).
文摘In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).
文摘This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).
文摘In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).
