共查询到10条相似文献,搜索用时 93 毫秒
1.
José Marí a Martell Carlos Pé rez Rodrigo Trujillo-Gonzá lez 《Transactions of the American Mathematical Society》2005,357(1):385-396
We show that the classical Hörmander condition, or analogously the -Hörmander condition, for singular integral operators is not sufficient to derive Coifman's inequality
where , is the Hardy-Littlewood maximal operator, is any weight and is a constant depending upon and the constant of . This estimate is well known to hold when is a Calderón-Zygmund operator.
where and where is an arbitrary weight. However, by a recent result due to A. Lerner, this inequality is satisfied whenever is a Calderón-Zygmund operator.
where , is the Hardy-Littlewood maximal operator, is any weight and is a constant depending upon and the constant of . This estimate is well known to hold when is a Calderón-Zygmund operator.
As a consequence we deduce that the following estimate does not hold:
where and where is an arbitrary weight. However, by a recent result due to A. Lerner, this inequality is satisfied whenever is a Calderón-Zygmund operator.
One of the main ingredients of the proof is a very general extrapolation theorem for weights.
2.
Adam Nyman 《Transactions of the American Mathematical Society》2005,357(4):1349-1416
Let be a smooth scheme of finite type over a field , let be a locally free -bimodule of rank , and let be the non-commutative symmetric algebra generated by . We construct an internal functor, , on the category of graded right -modules. When has rank 2, we prove that is Gorenstein by computing the right derived functors of . When is a smooth projective variety, we prove a version of Serre Duality for using the right derived functors of .
3.
David J. Pengelley Frank Williams 《Transactions of the American Mathematical Society》2000,352(4):1453-1492
The mod 2 Steenrod algebra and Dyer-Lashof algebra have both striking similarities and differences arising from their common origins in ``lower-indexed' algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra , whose module actions are equivalent to, but quite different from, those of and . The exact relationships emerge as ``sheared algebra bijections', which also illuminate the role of the cohomology of . As a bialgebra, has a particularly attractive and potentially useful structure, providing a bridge between those of and , and suggesting possible applications to the Miller spectral sequence and the structure of Dickson algebras.
4.
Naihuan Jing Kailash C. Misra 《Transactions of the American Mathematical Society》1999,351(4):1663-1690
We construct explicitly the -vertex operators (intertwining operators) for the level one modules of the classical quantum affine algebras of twisted types using interacting bosons, where for (), for , for (), and for (). A perfect crystal graph for is constructed as a by-product.
5.
Lia Petracovici 《Transactions of the American Mathematical Society》2005,357(9):3481-3491
Let , , and let denote the sequence of convergents to the regular continued fraction of . Let be a function holomorphic at the origin, with a power series of the form . We assume that for infinitely many we simultaneously have (i) , (ii) the coefficients stay outside two small disks, and (iii) the series is lacunary, with for . We then prove that has infinitely many periodic orbits in every neighborhood of the origin.
6.
Megumi Harada Nicholas Proudfoot 《Transactions of the American Mathematical Society》2005,357(4):1445-1467
Given an -tuple of positive real numbers , Konno (2000) defines the hyperpolygon space , a hyperkähler analogue of the Kähler variety parametrizing polygons in with edge lengths . The polygon space can be interpreted as the moduli space of stable representations of a certain quiver with fixed dimension vector; from this point of view, is the hyperkähler quiver variety defined by Nakajima. A quiver variety admits a natural -action, and the union of the precompact orbits is called the core. We study the components of the core of , interpreting each one as a moduli space of pairs of polygons in with certain properties. Konno gives a presentation of the cohomology ring of ; we extend this result by computing the -equivariant cohomology ring, as well as the ordinary and equivariant cohomology rings of the core components.
7.
Ethan Akin 《Transactions of the American Mathematical Society》2005,357(7):2681-2722
While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure is the countable dense subset is clopen of the unit interval. It is a topological invariant for the measure. For the class of good measures it is a complete invariant. A full, nonatomic measure is good if whenever are clopen sets with , there exists a clopen subset of such that . These measures have interesting dynamical properties. They are exactly the measures which arise from uniquely ergodic minimal systems on Cantor space. For some of them there is a unique generic measure-preserving homeomorphism. That is, within the Polish group of such homeomorphisms there is a dense, conjugacy class.
8.
For any maximal coaction and any closed normal subgroup of , there exists an imprimitivity bimodule between the full crossed product and , together with compatible coaction of . The assignment implements a natural equivalence between the crossed-product functors `` ' and `` ', in the category whose objects are maximal coactions of and whose morphisms are isomorphism classes of right-Hilbert bimodule coactions of .
9.
Robert R. Bruner Lê M. Hà Nguyê n H. V. Hung 《Transactions of the American Mathematical Society》2005,357(2):473-487
Let be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer . It has been shown that the algebraic transfer is highly nontrivial and, more precisely, that is an isomorphism for . However, Singer showed that is not an epimorphism. In this paper, we prove that does not detect the nonzero element for every . As a consequence, the localized given by inverting the squaring operation is not an epimorphism. This gives a negative answer to a prediction by Minami.
10.
Huy Tà i Hà Ngô Viê t Trung 《Transactions of the American Mathematical Society》2005,357(9):3655-3672
This paper addresses problems on arithmetic Macaulayfications of projective schemes. We give a surprising complete answer to a question poised by Cutkosky and Herzog. Let be the blow-up of a projective scheme along the ideal sheaf of . It is known that there are embeddings for , where denotes the maximal generating degree of , and that there exists a Cohen-Macaulay ring of the form (which gives an arithmetic Macaulayfication of ) if and only if , for , and is equidimensional and Cohen-Macaulay. We show that under these conditions, there are well-determined invariants and such that is Cohen-Macaulay for all d(I)e + \varepsilon$"> and e_0$">, and that these bounds are the best possible. We also investigate the existence of a Cohen-Macaulay Rees algebra of the form . If has negative -invariant, we prove that such a Cohen-Macaulay Rees algebra exists if and only if , for 0$">, and is equidimensional and Cohen-Macaulay. Moreover, these conditions imply the Cohen-Macaulayness of for all d(I)e + \varepsilon$"> and e_0$">.