A boundedness criterion is set up for some convolution operators on a compact Lie group.By this criterion a Hormander multiplier theorem is proved in the Hardy spaces on SU(2).
Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearl...Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.展开更多
An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict effi...An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.展开更多
In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is establis...In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.展开更多
In this paper, we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn ×Rm. Under the condition that Ω is a function in certain block spaces, which is optimal in some senses, the ...In this paper, we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn ×Rm. Under the condition that Ω is a function in certain block spaces, which is optimal in some senses, the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.展开更多
The main purpose of this paper is to extend to classical groups a H*irmander multiplier theorem concerning translation invariant operators on L p spaces which are known for the n-torus.
We study the regularity and convergence of solutions for the n-dimensional(n=2,3)fourth-order vector-valued Helmholtz equations u-βΔu+γ(-Δ)^(2)u=v for a given v in several Sobolev spaces,whereβ>0 andγ>0 ar...We study the regularity and convergence of solutions for the n-dimensional(n=2,3)fourth-order vector-valued Helmholtz equations u-βΔu+γ(-Δ)^(2)u=v for a given v in several Sobolev spaces,whereβ>0 andγ>0 are two given constants.By making use of the Fourier multiplier theorem,we establish the regularity and the L_(p)-L_(9)estimates of solutions for Eq.(VFHE)under the condition v∈L_(P)(R^(n)).We then derive the convergence that a solution u of Eq.(VFHE)approaches v weakly in L_(P)(R^(n))and strongly in L^(q)(R^(n))as the parameter pair(β,γ)approaches(0,0).In particular,as an application of the above results,for(v,u)solving the following viscous incompressiblefluid equations{div v=div u=0,v(t)+u·△V+V·△u^(T)+·△P=V△V(INS)We gain the strong convergence in L^(∞)([0,T],L^(s)(R^(n)))from the Eqs.(VFHE)-(INS)to the Navier-Stokes equations as the parameter pair(β,γ)tending to(0,0),where s=2h/(h-2)withh>n.展开更多
文摘A boundedness criterion is set up for some convolution operators on a compact Lie group.By this criterion a Hormander multiplier theorem is proved in the Hardy spaces on SU(2).
文摘Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.
基金Supported by the National Natural Science Foundation of China(10461007)Supported by the Natural Science Foundation of Jiangxi Province(0611081)
文摘An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.
基金the Natural Science Foundation of Zhejiang Province,China(M103089)
文摘In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.
基金Supported by National Natural Science Foundation of China (Grant No. G11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘In this paper, we study the generalized Marcinkiewicz integral operators MΩ,r on the product space Rn ×Rm. Under the condition that Ω is a function in certain block spaces, which is optimal in some senses, the boundedness of such operators from Triebel-Lizorkin spaces to Lp spaces is obtained.
文摘The main purpose of this paper is to extend to classical groups a H*irmander multiplier theorem concerning translation invariant operators on L p spaces which are known for the n-torus.
基金supported by the National Natural Science Foundation of China under grants(No.11626156)supported by the Natural Science Foundation of Tianjin(No.20JCYBJC01410).
文摘We study the regularity and convergence of solutions for the n-dimensional(n=2,3)fourth-order vector-valued Helmholtz equations u-βΔu+γ(-Δ)^(2)u=v for a given v in several Sobolev spaces,whereβ>0 andγ>0 are two given constants.By making use of the Fourier multiplier theorem,we establish the regularity and the L_(p)-L_(9)estimates of solutions for Eq.(VFHE)under the condition v∈L_(P)(R^(n)).We then derive the convergence that a solution u of Eq.(VFHE)approaches v weakly in L_(P)(R^(n))and strongly in L^(q)(R^(n))as the parameter pair(β,γ)approaches(0,0).In particular,as an application of the above results,for(v,u)solving the following viscous incompressiblefluid equations{div v=div u=0,v(t)+u·△V+V·△u^(T)+·△P=V△V(INS)We gain the strong convergence in L^(∞)([0,T],L^(s)(R^(n)))from the Eqs.(VFHE)-(INS)to the Navier-Stokes equations as the parameter pair(β,γ)tending to(0,0),where s=2h/(h-2)withh>n.
