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1.
Huaquan Wei Yanming Wang Yangming Li 《Proceedings of the American Mathematical Society》2004,132(8):2197-2204
This paper proves: Let be a saturated formation containing . Suppose that is a group with a normal subgroup such that .
(1) If all maximal subgroups of any Sylow subgroup of are -supple- mented in , then ;
(2) If all minimal subgroups and all cyclic subgroups with order 4 of are -supplemented in , then .
2.
On commutators of fractional integrals 总被引:1,自引:0,他引:1
Xuan Thinh Duong Li Xin Yan 《Proceedings of the American Mathematical Society》2004,132(12):3549-3557
Let be the infinitesimal generator of an analytic semigroup on with Gaussian kernel bounds, and let be the fractional integrals of for . For a BMO function on , we show boundedness of the commutators from to , where . Our result of this boundedness still holds when is replaced by a Lipschitz domain of with infinite measure. We give applications to large classes of differential operators such as the magnetic Schrödinger operators and second-order elliptic operators of divergence form.
3.
Edward Bierstone 《Proceedings of the American Mathematical Society》2004,132(4):997-1003
Let : denote a real analytic function on an open subset of , and let denote the points where does not admit a local analytic extension. We show that if is semialgebraic (respectively, globally subanalytic), then is semialgebraic (respectively, subanalytic) and extends to a semialgebraic (respectively, subanalytic) neighbourhood of . (In the general subanalytic case, is not necessarily subanalytic.) Our proof depends on controlling the radii of convergence of power series centred at points in the image of an analytic mapping , in terms of the radii of convergence of at points , where denotes the Taylor expansion of at .
4.
Caroline Sweezy 《Proceedings of the American Mathematical Society》2004,132(12):3599-3606
The relationship of the Hardy space and the space of integrable functions is examined in terms of intermediate spaces of functions that are described as sums of atoms. It is proved that these spaces have dual spaces that lie between the space of functions of bounded mean oscillation, , and . Furthermore, the spaces intermediate to and are shown to be dual to spaces similar to the space of functions of vanishing mean oscillation. The proofs are extensions of classical proofs.
5.
Let be a formal power series ring over a field of characteristic zero and any ideal. The aim of this work is to introduce some numerical invariants of the local rings by using the theory of algebraic -modules. More precisely, we will prove that the multiplicities of the characteristic cycle of the local cohomology modules and , where is any prime ideal that contains , are invariants of .
6.
Tsemo Aristide 《Proceedings of the American Mathematical Society》2004,132(12):3697-3702
A affine manifold is an -dimensional affine manifold whose linear holonomy lies in the similarity Lorentzian group but not in the Lorentzian group. In this paper, we show that a compact affine manifold is incomplete. Let be the Lorentz form, and the map on defined by . We show that for a compact radiant affine manifold , if a connected component of intersects the image of the universal cover of by the developing map, then either or a connected component of , where is a hyperplane, is contained in this image.
7.
Hal Schenck 《Proceedings of the American Mathematical Society》2004,132(12):3509-3512
Associated to an -dimensional integral convex polytope is a toric variety and divisor , such that the integral points of represent . We study the free resolution of the homogeneous coordinate ring as a module over . It turns out that a simple application of Green's theorem yields good bounds for the linear syzygies of a projective toric surface. In particular, for a planar polytope , satisfies Green's condition if contains at least lattice points.
8.
Reza Sazeedeh 《Proceedings of the American Mathematical Society》2004,132(10):2885-2891
In this paper we assume that is a Gorenstein Noetherian ring. We show that if is also a local ring with Krull dimension that is less than or equal to 2, then for any nonzero ideal of , is Gorenstein injective. We establish a relation between Gorenstein injective modules and local cohomology. In fact, we will show that if is a Gorenstein ring, then for any -module its local cohomology modules can be calculated by means of a resolution of by Gorenstein injective modules. Also we prove that if is -Gorenstein, is a Gorenstein injective and is a nonzero ideal of , then is Gorenstein injective.
9.
Brent J. Carswell 《Proceedings of the American Mathematical Society》2003,131(4):1233-1241
In both the Bergman space and the Hardy space , the problem of determining which bounded univalent mappings of the unit disk have the wandering property is addressed. Generally, a function in has the wandering property in , where denotes either or , provided that every -invariant subspace of is generated by the orthocomplement of within . It is known that essentially every function which has the wandering property in either space is the composition of a univalent mapping with a classical inner function, and that the identity mapping has this property in both spaces. Consequently, weak-star generators of also have the wandering property in both settings. The present paper gives a partial converse to this, and shows that in both settings there is a large class of bounded univalent mappings which fail to have the wandering property.
10.
Sandy Grabiner 《Proceedings of the American Mathematical Society》2004,132(6):1675-1684
Suppose that is a weighted convolution algebra on with the weight normalized so that the corresponding space of measures is the dual space of the space of continuous functions. Suppose that is a continuous nonzero homomorphism, where is also a convolution algebra. If is norm dense in , we show that is (relatively) weak dense in , and we identify the norm closure of with the convergence set for a particular semigroup. When is weak continuous it is enough for to be weak dense in . We also give sufficient conditions and characterizations of weak continuity of . In addition, we show that, for all nonzero in , the sequence converges weak to 0. When is regulated, converges to 0 in norm.
11.
Arc-analytic roots of analytic functions are Lipschitz 总被引:2,自引:0,他引:2
Krzysztof Kurdyka Laurentiu Paunescu 《Proceedings of the American Mathematical Society》2004,132(6):1693-1702
Let be an arc-analytic function (i.e., analytic on every analytic arc) and assume that for some integer the function is real analytic. We prove that is locally Lipschitz; even if is less than the multiplicity of . We show that the result fails if is only a , arc-analytic function (even blow-analytic), . We also give an example of a non-Lipschitz arc-analytic solution of a polynomial equation , where are real analytic functions.
12.
Cristian D. Gonzalez-Avilé s 《Proceedings of the American Mathematical Society》2000,128(4):953-961
Let be a finite Galois extension of number fields with Galois group , let be an abelian variety defined over , and let and denote, respectively, the Tate-Shafarevich groups of over and of over . Assuming that these groups are finite, we derive, under certain restrictions on and , a formula for the order of the subgroup of of -invariant elements. As a corollary, we obtain a simple formula relating the orders of , and when is a quadratic extension and is the twist of by the non-trivial character of .
13.
Igor Fulman Paul S. Muhly Dana P. Williams 《Proceedings of the American Mathematical Society》2004,132(3):707-717
Let be a second countable, locally compact groupoid with Haar system, and let be a bundle of -algebras defined over the unit space of on which acts continuously. We determine conditions under which the associated crossed product is a continuous trace -algebra.
14.
Let , , be a bounded smooth connected open set and be a map satisfying the hypotheses (H1)-(H4) below. Let with , in and with be two weak solutions of
Suppose that in . Then we show that u_1$"> in under the following assumptions: either u_1$"> on , or on and in . We also show a measure-theoretic version of the Strong Comparison Principle.
Suppose that in . Then we show that u_1$"> in under the following assumptions: either u_1$"> on , or on and in . We also show a measure-theoretic version of the Strong Comparison Principle.
15.
Julien Cassaigne Alain Plagne 《Proceedings of the American Mathematical Society》2004,132(10):2833-2840
An exact additive asymptotic basis is a set of nonnegative integers such that there exists an integer with the property that any sufficiently large integer can be written as a sum of exactly elements of . The minimal such is the exact order of (denoted by ). Given any exact additive asymptotic basis , we define to be the subset of composed with the elements such that is still an exact additive asymptotic basis. It is known that is finite.
In this paper, we introduce a new and simple method for the study of this function. We obtain a new estimate from above for which improves drastically and in any case on all previously known estimates. Our estimate, namely , cannot be too far from the truth since verifies . However, it is certainly not always optimal since . Our last result shows that is in fact a strictly increasing sequence.
In this framework, a central quantity introduced by Grekos is the function defined as the following maximum (taken over all bases of exact order ):
In this paper, we introduce a new and simple method for the study of this function. We obtain a new estimate from above for which improves drastically and in any case on all previously known estimates. Our estimate, namely , cannot be too far from the truth since verifies . However, it is certainly not always optimal since . Our last result shows that is in fact a strictly increasing sequence.
16.
Huaxin Lin 《Proceedings of the American Mathematical Society》2004,132(11):3215-3224
Let be a non-unital and -unital simple -algebra. We show that if is simple, then is purely infinite. We also show that is simple if and only if has a continuous scale provided that is not isomorphic to the compact operators.
17.
Alex N. Dranishnikov Yuli B. Rudyak 《Proceedings of the American Mathematical Society》2005,133(5):1557-1561
We construct closed -connected manifolds of dimensions that possess non-trivial rational Massey triple products. We also construct examples of manifolds such that all the cup-products of elements of vanish, while the group is generated by Massey products: such examples are useful for the theory of systols.
18.
A. Picó n C. Piñ eiro 《Proceedings of the American Mathematical Society》2004,132(10):2893-2898
Let a Banach space and a -algebra of subsets of a set . We say that a vector measure Banach space has the bounded Vitaly-Hahn-Sacks Property if it satisfies the following condition: Every vector measure , for which there exists a bounded sequence in verifying for all , must belong to . Among other results, we prove that, if is a vector measure Banach space with the bounded V-H-S Property and containing a complemented copy of , then contains a copy of .
19.
In this paper, we prove that if is a non-elementary subgroup of , with , then the eigenvalue field of has infinite degree over .
20.
Takahiko Nakazi 《Proceedings of the American Mathematical Society》2003,131(4):1267-1271
and denote the Hardy spaces on the open unit disc . Let be a function in and . If is an inner function and , then is orthogonal in . W.Rudin asked if the converse is true and C. Sundberg and C. Bishop showed that the converse is not true. Therefore there exists a function such that is not an inner function and is orthogonal in . In this paper, the following is shown: is orthogonal in if and only if there exists a unique probability measure on [0,1] with supp such that for nearly all in where is the Nevanlinna counting function of . If is an inner function, then is a Dirac measure at .