C~n中F(p,q,s)型空间上的Bergman型算子

设p0,s≥0,q+s-1,q+n-1.讨论了C~n中单位球上F(p,q,s)到本身或A(p,q,s)空间到L(p,q,s)空间上的Bergman型算子的有界性条件.     

C~n中F(p,q,s)空间的等价刻画及应用

设0相似文献   

单位球上Bloch型空间到F(p,q,s)空间的Volterra复合算子

记H(B)为C~n中单位球B上的解析函数空间.设φ为B到自身的解析映射,g∈H(B),μ为正规权,定义Volterra复合算子为(V_φ~gf)(z)=∫_0~1f(φ(tz))Rg(tz)dt/t.本文考虑Volterra复合算子V_φ~g从B_μ或B_(μ,0)空间到F(p,q,s)或F_0(p,q,s)空间上的有界性和紧性,得出了算子V_φ~g:B_μ(B_(μ,0))→F(p,q,s)或B_μ(B_(μ,0))→F_0(p,q,s)的紧性与有界性等价.同时,也给出了算子V_φ~g从B~α或B_0~α空间到F(p,q,s)或F_0(p,q,s)空间上的紧性和有界性刻画.     

广义加权Bloch空间与QK(p,q)空间之间的复合算子

设φ是复平面上的单位圆盘D上的全纯自映射,0＜p＜∞,q＞-2,α＞0.本文给出广义加权Bloch空间与QK(p,q)空间之间的复合算子的有界性和紧性.     

单位球上F(p,q,s)空间的分解和刻画

设p>0,s ≥ 0,q>max{-n-1,-s-1},本文探讨了单位球上F（p,q,s）空间的一种等价刻画和分解问题.具体结果为：（1） f∈ F（p,q,s）当且仅当f∈ H（B）,且I^p=sup_a∈B∫_B|R^α,γf（z）|^p（1-|z|²）^q+pγ-p（1-|φ_a（z）|²）^sdv（z）<∞,其中α>-1 和γ>max{0,1-（q+s+1）/p,1-（q+n+1）/p}. （2） 若{d_k}∈ ∫^p,则存在序列{w_k}⊂B,使得 f（z）=∑_k=1^∞（d_k（1-|w_k|²）^t+1）/（1-k>）^{t+（q+n+1）/p}）（z∈B）属于F（p,q,s）,其中t>max{1-1/p,0}（q+n+1）+max{1/p,1}s-1.     

从β0到E(p,q)和E0(p,q)空间的复合算子

设ψ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子Cψ:Cψ(f)=foψ.我们利用从β0到E(p,q)和E0(p,q)空间的复合算子研究了空间E(p,q)和E0(p,q),给出了-个新的特征.     

Gleason问题在多复变F(p,q,s)空间上的可解性

在0p∞,0≤s∞,max{-n-1,-s-1}q∞的条件下,证明了Gleason问题在C~n中以单位球为支撑集的一般函数空间F(p,q,s)上是可解的.     

F(p,q,s)空间的嵌入关系

为得到一类广泛的解析函数空间F(p,q,s)之间的嵌入关系,将每个空间F(p,q,s)对应为三维空间R(F)中一点(p,q,s),从而将空间之间的嵌入关系转化为三维空间中直线的单调性进行了研究,完善了已有的结果.     

C~n单位球中F(p,q,s)空间上的原子分解

该文主要研究C~n单位球中F(p,q,s)空间上的原子分解,而F(p,q,s)空间包含许多重要的函数空间,比如Bloch空间、BMOA空间和近年来新引入的Q_s空间.该文主要借助s-Carleson测度和Schur定理研究了C~n单位球中F(p,q,s)空间在1p∞情形下的原子分解.     

模p Steenrod代数上同调的一些注记

模p Steenrod代数A的上同调H~(s,t)(A)是决定球面稳定同伦群的最有力数据.首先给出了模p Steenrod代数A和May谱序列的一些重要结论,而后给出与乘积元γ_(s+3)l_ng_0∈H~(s+8,t(s,n))(A)密切相关的May谱E_1项的结果,这些结论对该乘积元的非平凡性研究有重要意义,其中t(s,n)=p~(n+1)q+2p~nq+(s+3)p~2q+(s+3)pq+(s+3)q+s, 0≤sp-6, n≥4, p≥11, q=2(p-1).     

On (q 2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)

A (k,n)-arc in PG(2,q) is usually defined to be a set of k points in the plane such that some line meets in n points but such that no line meets in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow to be a multiset, that is, permit to contain multiple points. The case k=q ²+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q ²+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q ²+q+2 and minimum distance q ². Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q ²+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem.     

M p(G)≠M q(G) (p −1+q −=1)

There exists a compact groupG havingM _4/3(G)≠M ₄(G). This answers in the negative (the dual reformulation of) a question of Eymard (Séminaire Bourbaki, 1969/70).     

Complete and Stable O(p+1)×O(q+1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space ℝ p+q+2

We classify the zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in the euclidean space ℝ ^p+q+2, p,q > 1, analyzing whether they are embedded and stable. The Morse index of the complete hypersurfaces show the existence of embedded, complete and globally stable zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in ℝ ^p+q+2, p+q≥ 7, which are not homeomorphic to ℝ ^p+q+1. Such stable examples provide counter-examples to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature. Mathematics Subject Classifications (2000): 53A10, 53C42,49005.     

Pullback functors for reduced and unreduced $$L^{q,p}$$ L q,p -cohomology

Annals of Global Analysis and Geometry - In Stanciu (Ann Global Anal Geom 56:245-275, 2019), we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of...     

Geometric and pseudo-geometric graphs (q2+1,q+1,1)

Let ₀ be a particular vertex of a strongly regular graph G with parameters v, n₁, p ₁₁ ¹ p ₁₁ ¹ . Let A be the adjacency matrix of G, and B the submatrix of A whose rows correspond to the vertices of G adjacent to ₀ and whose columns correspond to the vertices of G nonadjacent to ₀. Then the designD(₀) with incidence matrix B has the parameters v=n₁ b=v-n₁–1, r=n₁–p^11/1–1, k = p ₁₁ ² . In this paper we study the connection between G andD(₀) when the graph G is geometric or pseudo-geometric (q²+1,q+1,1).The research of this author was supported by the National Science Foundation Grant No. GP 23520 and the U.S. Air Force Office of Scientific Research under Grant No. AFOSR-68-1415C.The research of this author was supported by the National Science Foundation Grant No. GP 17172, while he was visiting professor at Stanford University.     

Elementary aspects ofB p,q s (Kn) andF p,q s (Kn) spaces

In the first part of this paper, we discuss some properties of S^Ω(K_n), L _P ^Ω (K_n) and L _P ^Ω (K_n;l_q) spaces, give the Plancherel-Polya-Nikol’skij type inequalities and some multiplier theorems. In the second part of this paper, using the results of Part I we prove some preliminary results for the spaces B _p,q ^s (K_n) and F _p,q ^s (K_n).     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where