We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating v...We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating varieties.展开更多
In this note,we obtain some a-priori estimates for gradient of weak solutions to a class of subelliptic quasilinear equations constructed by Ho¨rmander’s vector fields,and then prove local uniqueness of weak sol...In this note,we obtain some a-priori estimates for gradient of weak solutions to a class of subelliptic quasilinear equations constructed by Ho¨rmander’s vector fields,and then prove local uniqueness of weak solutions.A key ingredient is the estimated about kernel on metirc ＂annulus＂.展开更多
In this paper,we consider the(q,r)boundedness ofthe pseudo-differential operators with the amplitude a∈L^(P)S_(p)^(m)(p≥1,m∈R,0≤p≤1).When 0<r≤∞,1≤p,q≤∞,r≤p,1/r≤1/p+1/q,we provethat if m<(n(p-1))/min(...In this paper,we consider the(q,r)boundedness ofthe pseudo-differential operators with the amplitude a∈L^(P)S_(p)^(m)(p≥1,m∈R,0≤p≤1).When 0<r≤∞,1≤p,q≤∞,r≤p,1/r≤1/p+1/q,we provethat if m<(n(p-1))/min(min{2,p,q})-np((1/p)+(1/q)-(1/r))then for any a∈L^(p)S_(p)^(m),the pseudo-differential operator T_(a)is bounded from L^(q)to L^(r).It is a generalization and improvement of the known theorems and in general the conditions on r,m are sharp.展开更多
文摘We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating varieties.
基金Supported by the National Natural Science Foundation of China (Grant No. 10871157)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200806990032)the Keji Chuangxin Jijin of Northwestern Polytechnical University (Grant No. 2008KJ02033)
文摘In this note,we obtain some a-priori estimates for gradient of weak solutions to a class of subelliptic quasilinear equations constructed by Ho¨rmander’s vector fields,and then prove local uniqueness of weak solutions.A key ingredient is the estimated about kernel on metirc ＂annulus＂.
文摘In this paper,we consider the(q,r)boundedness ofthe pseudo-differential operators with the amplitude a∈L^(P)S_(p)^(m)(p≥1,m∈R,0≤p≤1).When 0<r≤∞,1≤p,q≤∞,r≤p,1/r≤1/p+1/q,we provethat if m<(n(p-1))/min(min{2,p,q})-np((1/p)+(1/q)-(1/r))then for any a∈L^(p)S_(p)^(m),the pseudo-differential operator T_(a)is bounded from L^(q)to L^(r).It is a generalization and improvement of the known theorems and in general the conditions on r,m are sharp.
