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1.
Reducing Subspaces for a Class of Multiplication Operators   总被引:4,自引:0,他引:4  
Let D be the open unit disk in the complex plane C. The Bergmanspace is the Hilbert space of analytic functions f in D such that where dA is the normalized area measure on D. If are two functions in , then the inner product of f and g is given by We study multiplication operators on induced by analytic functions. Thus for H (D), the space ofbounded analytic functions in D, we define by It is easy to check that M is a bounded linear operator on with ||M||=||||=sup{|(z)|:zD}.  相似文献   

2.
Ramanujan claimed in his first letter to Hardy (16 January 1913)that where (k) lies between 2/21 and 8/45. This conjecture was provedin 1995 by Flajolet et al. The paper establishes the followingrefinement. where Both bounds for *(k) are sharp.  相似文献   

3.
In this paper we introduce the one-sided sharp functions dennedby and where z+ = max(z, 0). We study the BMO spaces associatedto and and their relation with the good weights for theone-sided Hardy-Littlewood maximal functions. Finally, as anapplication of our results, we characterize the weights forone-sided fractional integrals and one-sided fractional maximaloperators.  相似文献   

4.
Ergodicity of a Class of Cocycles Over Irrational Rotations   总被引:1,自引:0,他引:1  
It is proved that if is irrational and L2(S1) with o(l/n)then for each mZ\{0} the corresponding skew product is ergodic. The rigidity of specialflows over irrational rotations with roof functions whose Fouriercoefficients are in o(l/n) is also shown.  相似文献   

5.
Let E be a Banach space of functions on a locally compact Abeliangroup G satisfying certain conditions. It has been proved thatfor every bounded operator M on E commuting with translationsthere exists such that , where is a suitable subset of the group of the continuous morphismsfrom G into * and is a generalized Fourier transform of g defined on .  相似文献   

6.
Let G be a graph of order 2n + l having maximum degree 2n –1. We prove that the total chromatic number of G is 2n if andonly if e + ' n, where w is a vertex of minimum degree in G, is the complement of Gw, e is the size of , and ' is the edge independence number of .  相似文献   

7.
We present here a technique for establishing inequalities ofthe form in the set of alltrigonometric polynomials of order n which have only real zeros.The function is assumed to be convex and increasing on [0,). As a corollary of the main result we get Turan's inequalities with the exact constantc(n, k, q) for each 1 q , n and k.  相似文献   

8.
Inverse Sturm–Liouville problems with eigenparameter-dependentboundary conditions are considered. Theorems analogous to thoseof both Hochstadt and Gelfand and Levitan are proved. In particular, let ly = (1/r)(–(py')'+qy), , where det = > 0, c 0, det > 0, t 0 and (cs + drautb)2 < 4(crta)(dsub). Denoteby (l; ; ) the eigenvalue problem ly = y with boundary conditionsy(0)cos+y'(0)sin = 0 and (a+b)y(1) = (c+d)(py')(1). Define (; ; ) as above but with l replacedby . Let wn denote the eigenfunctionof (l; ; ) having eigenvalue n and initial conditions wn(0)= sin and pw'n(0) = –cos and let n = –awn(1)+cpw'n(1).Define n and n similarly. As sample results, it is proved that if (l; ; ) and (; ; ) have the same spectrum, and (l;; ) and (; ; ) have the samespectrum or for all n, thenq/r = /.  相似文献   

9.
The paper shows that, if the operator T:A()B() is compact foralmost every , then is compact when or is the interpolation functor constructed for infinitefamilies of Banach spaces and S satisfies certain conditions.  相似文献   

10.
Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators   总被引:2,自引:0,他引:2  
Necessary and sufficient conditions for the boundedness from to of Volterra integral operators of the form where k(x,y) is a non-negative kernel under suitablemonotone conditions, are given. The cases 1 <p q < ,1 < q < p < and 0 < q < l < p < are considered.The results extend the well-known weighted norm Hardy inequality.  相似文献   

11.
Let w(x), u(x) and (x) be weight functions. In this paper, underappropriate conditions on Young's functions 1, 2 we characterizethe inequality for the Hardy-typeoperator T defined in [1] and the inequality for the fractional maximal operator M, ; definedin [8], as well as the corresponding weak-type inequalities.  相似文献   

12.
Let R2 be a bounded Lipschitz domain and let be a Carathèodory integrand such that F(x,·) is polyconvex for L2-a.e. x . Moreover assume thatF is bounded from below and satisfies the condition as det for L2-a.e. x . The paper describes the effect of domain topologyon the existence and multiplicity of strong local minimizersof the functional wherethe map u lies in the Sobolev space Wid1,p (, R2) with p 2and satisfies the pointwise condition u(x) >0 for L2-a.e.x . The question is settled by establishing that F[·]admits a set of strong local minimizers on that can be indexed by the group Pn Zn, the directsum of Artin's pure braid group on n strings and n copies ofthe infinite cyclic group. The dependence on the domain topologyis through the number of holes n in and the different mechanismsthat give rise to such local minimizers are fully exploitedby this particular representation.  相似文献   

13.
Link Polynomials of Higher Order   总被引:1,自引:0,他引:1  
In this paper, we study certain polynomial invariants of links(singular or non-singular) that are related to the Homfly polynomialand Vassiliev's invariants. The Homfly polynomial HL [3] (alsoknown as the Flypmoth polynomial) satisfies the well-known skeinrelation The Vassiliev invariants [1, 2] (of order 1) satisfy the relations and The invariants that we study satisfy the skein relations   相似文献   

14.
For bounded Hilbert space operators X, An and Bn, n = 1, 2,..., for all p < and These inequalities involve some estimates for the norm of elementaryoperators with the range contained in the Schatten p-ideals.  相似文献   

15.
Let F be a germ of a holomorphic function at 0 in Cn+1, having0 as a critical point not necessarily isolated, and let be a germ of a holomorphic vectorfield at 0 in Cn+1 with an isolated zero at 0, and tangent toV := F–1(0). Consider the OV,0-complex obtained by contractingthe germs of Kähler differential forms of V at 0 (0.1) with the vector field X:=|Von V: (0.2)  相似文献   

16.
Let (s, ) be the Hurwitz zeta function with parameter . Powermean values of the form are studied, where q and h are positive integers. These mean valuescan be written as linear combinations of , where r(s1,...,sr;) is a generalization of Euler–Zagiermultiple zeta sums. The Mellin–Barnes integral formulais used to prove an asymptotic expansion of , with respect to q. Hence a general way of deducingasymptotic expansion formulas for is obtained. In particular, the asymptotic expansion of with respect to q is written down.  相似文献   

17.
It is well known that there are bounded domains Rn whose boundaries are not smooth enough for there to exist a bounded linear extensionfor the Sobolev space into , but the embedding is nevertheless compact. For the Lipboundaries (0<<1) studied in [3, 4], there does not existin general an extension operator of into but there is a bounded linear extension of into and the smoothness retained by thisextension is enough to ensure that the embedding is compact. It is natural to ask if this is typicalfor bounded domains which are such that is compact, that is, that there exists a boundedextension into a space of functions in Rn which enjoy adequatesmoothness. This is the question which originally motivatedthis paper. Specifically we study the ‘extension by zero’operator on a space of functions with given ‘generalized’smoothness defined on a domain with an irregular boundary, anddetermine the target space with respect to which it is bounded.  相似文献   

18.
We characterize the mapping properties such as the boundedness,compactness and measure of noncompactness for those real weightfunctions , , u0, v0, for which the Hardy-type integral operatorof the form acts from to , when the parameters are restricted to the range 1 < max (r,s) min (p, q) < and the kernel k(x, y) 0 satisfies theOinarov condition (see (2) below). For the case k(x, y) = 1,we obtain lower and upper estimates of the approximation numbers,extending the result of [5].  相似文献   

19.
The existence of 2-periodic solutions of the second-order differentialequation where a, b satisfy and p(t)=p(t+2),t R, is examined. Assume that limits limx±F(x)=F(±)(F(x)=) and limx±g(x)=g(±)exist and are finite. It is proved that the equation has atleast one 2-periodic solution provided that the zeros of thefunction 1 are simple and the zeros of the functions 1, 2 aredifferent and the signs of 2 at the zeros of 1 in [0,2/n) donot change or change more than two times, where 1 and 2 aredefined as follows: Moreover, it is also proved that the given equation has at leastone 2-periodic solution provided that the following conditionshold: with 1 p < q 2.  相似文献   

20.
Interpolation of Vector-Valued Real Analytic Functions   总被引:2,自引:0,他引:2  
Let Rd be an open domain. The sequentially complete DF-spacesE are characterized such that for each (some) discrete sequence(zn) , a sequence of natural numbers (kn) and any family the infinite system of equations has an E-valued real analytic solution f.  相似文献   

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