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Some local properties defining To-groups and related classes of groups
http://ddd.uab.cat/record/144969
We call G a HallX -group if there exists a normal nilpotent subgroup N of G for which G/N0 is an X-group. We call G a T0-group provided G/Φ(G) is a T -group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define HallX -groups and T0-groups where X ∈ {T , PT , PST }; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations. 2010 Mathematics Subject Classification: Primary: 20D10, 20D20, 20D35. Ballester-Bolinches, A.Wed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449692016Extreme cycles :: the center of a Leavitt path algebra
http://ddd.uab.cat/record/144968
In this paper we introduce new techniques in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of the center. Extreme cycles appear for the first time; they concentrate the purely infinite part of a Leavitt path algebra and, jointly with the line points and vertices in cycles without exits, are the key ingredients in order to determine the center of a Leavitt path algebra. Our work will rely on our previous approach to the center of a prime Leavitt path algebra [13]. We will go further into the structure itself of the Leavitt path algebra. For example, the ideal I(Pec ∪ Pc ∪ Pl) generated by vertices in extreme cycles (Pec), by vertices in cycles without exits (Pc), and by line points (Pl) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to Pl ∪ Pc ∪ Pec. Hence its structure will contain much of the information about the Leavitt path algebra. In the row-finite case, we will need to add a new hereditary set: the set of vertices whose tree has infinite bifurcations (Pb∞). Corrales García, María G.Wed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449682016On the Galois correspondence theorem in separable Hopf Galois theory
http://ddd.uab.cat/record/144967
In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure. Crespo, TeresaWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449672016Upper bound for multi-parameter iterated commutators
http://ddd.uab.cat/record/144966
We show that the product BMO space can be characterized by iterated commutators of a large class of Calderón-Zygmund operators. This result followsfrom a new proof of boundedness of iterated commutators in terms of the BMO norm of their symbol functions, using Hytönen's representation theorem of Calderón-Zygmund operators as averages of dyadic shifts. The proof introduces some new paraproducts which have BMO estimates. Dalenc, LaurentWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449662016Mixed norm estimates for the Riesz transforms on SU (2)
http://ddd.uab.cat/record/144965
In this paper we prove mixed norm estimates for Riesz transforms on the group SU(2). From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced. Boggarapu, PradeepWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449652016Fine gradings on e6
http://ddd.uab.cat/record/144964
There are fourteenfine gradings on the exceptional Lie algebra e6 over an algebraically closed field of zero characteristic. We provide their descriptions and a proof that any fine grading is equivalent to one of them. Draper Fontanals, CristinaWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449642016Geometric characterizations of p-Poincaré inequalities in the metric setting
http://ddd.uab.cat/record/144963
We prove that a locally complete metric space endowed with a doubling measure satisfies an ∞-Poincar´e inequality if and only if given a null set, every two points can be joined by a quasiconvex curve which "almost avoids" that set. As an application, we characterize doubling measures on R satisfying an ∞-Poincaré inequality. For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincaré inequality for p > Q in terms of the p-modulus of quasiconvex curves connecting pairs of points in the space. A related characterization is given for the case Q − 1 < p ≤ Q. Durand-Cartagena, EstibalitzWed, 23 Dec 2015 07:06:31 GMThttp://ddd.uab.cat/record/1449632016Nilpotent groups of class three and braces
http://ddd.uab.cat/record/144962
New constructions of braces on finite nilpotent groups are given and hence this leads to new solutions of the Yang–Baxter equation. In particular, it follows that if a group G of odd order is nilpotent of class three, then it is a homomorphic image of the multiplicative group of a finite left brace (i. e. an involutive Yang–Baxter group) which also is a nilpotent group of class three. We give necessary and sufficient conditions for an arbitrary group H to be the multiplicative group of a left brace such that [H, H] ⊆ Soc(H) and H/[H, H] is a standard abelian brace, where Soc(H) denotes the socle of the brace H. Cedó, FerranWed, 23 Dec 2015 07:06:30 GMThttp://ddd.uab.cat/record/1449622016A nonlocal 1-Laplacian problem and median values
http://ddd.uab.cat/record/144961
In this paper, we study solutions to a nonlocal 1-Laplacian equation. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled. Mazón, José M.Wed, 23 Dec 2015 07:06:30 GMThttp://ddd.uab.cat/record/1449612016Nonlocal elliptic equations in bounded domains :: a survey
http://ddd.uab.cat/record/144960
In this paper we survey some results on the Dirichlet problem for nonlocal operators of the form. We start from the very basics, proving existence of solutions, maximum principles, and constructing some useful barriers. Then, we focus on the regularity properties of solutions, both in the interior and on the boundary of the domain. In order to include some natural operators L in the regularity theory, we do not assume any regularity on the kernels. This leads to some interesting features that are purely nonlocal, in the sense that they have no analogue for local equations. We hope that this survey will be useful for both novel and more experienced researchers in the field. Ros-Oton, XavierWed, 23 Dec 2015 07:06:30 GMThttp://ddd.uab.cat/record/1449602016Inequalities for poisson integrals with slowly growing dimensional constants
http://ddd.uab.cat/record/138626
Let Pt be the Poisson kernel. We study the following Lp inequality for the Poisson integral P f(x, t) = (Pt ∗ f)(x) with respect to a Carleson measure µ:. Grafakos, LoukasThu, 01 Oct 2015 08:21:35 GMThttp://ddd.uab.cat/record/1386262007Monoid rings that are firs
http://ddd.uab.cat/record/138535
It is well-known that the monoid ring of the free product of a free group and a free monoid over a skew field is a fir. We give a proof of this fact that is more direct than the proof in the literature. Pitarch, AndreuWed, 30 Sep 2015 14:59:01 GMThttp://ddd.uab.cat/record/1385351990Some remarks on almost finitely generated nilpotent groups
http://ddd.uab.cat/record/138533
We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp = Hp for all p. Then we have proper set-inclusions {fg} C {fg-like} C {fgp}. We examine the extent to which fg-hke nilpotent groups satisfy the axioms for a Serre class. We obtain a complete answer only in the case that [G, G] is finite . (The collection of fgp nilpotent groups is known te form a Serre class in the extended sense). Hilton, PeterWed, 30 Sep 2015 14:43:11 GMThttp://ddd.uab.cat/record/1385331992The fall of the doubling condition in Calderón-Zygmund theory
http://ddd.uab.cat/record/138529
The most important results of standard Calderón-Zygmund Theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral. Verdera, JoanWed, 30 Sep 2015 12:09:28 GMThttp://ddd.uab.cat/record/1385292002Multilinear singular integrals
http://ddd.uab.cat/record/138528
We survey the thoery of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson’s operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators. Thiele, Christoph M.Wed, 30 Sep 2015 12:01:30 GMThttp://ddd.uab.cat/record/1385282002Why the Riesz transforms are averages of the dyadic shifts?
http://ddd.uab.cat/record/138527
The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators —so-called dyadic shifts. We show here that the same is true in any Rn —the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new one. Petermichl, S.Wed, 30 Sep 2015 11:56:23 GMThttp://ddd.uab.cat/record/1385272002Singular integrals and rectifiability
http://ddd.uab.cat/record/138526
We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey on some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods. Mattila, PerttiWed, 30 Sep 2015 11:48:45 GMThttp://ddd.uab.cat/record/1385262002Poincaré inequalities and Sobolev spaces
http://ddd.uab.cat/record/138525
Our understsanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function. MacManus, PaulWed, 30 Sep 2015 11:42:54 GMThttp://ddd.uab.cat/record/1385252002Recent progress on the Kakeya conjecture
http://ddd.uab.cat/record/138524
We survey recent developments on the Kakeya problem. Katz, NetsWed, 30 Sep 2015 11:36:55 GMThttp://ddd.uab.cat/record/1385242002The solution of the Kato problem in two dimensions
http://ddd.uab.cat/record/138523
We solve, in two dimensions, the “square root problem of Kato”. That is, for L ≡ − div(A(x)∇), where A(x) is a 2 × 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2 : L2 1(R2) → L2(R2). Hofmann, SteveWed, 30 Sep 2015 11:29:45 GMThttp://ddd.uab.cat/record/1385232002Oscillatory and Fourier integral operators with degenerate canonical relations
http://ddd.uab.cat/record/138521
We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focusses on topics directly related to the work of the authors. Greenleaf, AllanWed, 30 Sep 2015 11:23:33 GMThttp://ddd.uab.cat/record/1385212002On multilinear singular integrals of Calderón-Zygmund type
http://ddd.uab.cat/record/138520
A variety of results regarding multilinear Calderón-Zygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur’s test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal operator associated with multilinear singular integrals is also introduced and employed to obtain weighted norm inequalities. Grafakos, LoukasWed, 30 Sep 2015 11:15:01 GMThttp://ddd.uab.cat/record/1385202002Directional operators and mixed norms
http://ddd.uab.cat/record/138519
We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calder´on and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting questions remain unanswered. Duoandikoetxea, JavierWed, 30 Sep 2015 11:08:33 GMThttp://ddd.uab.cat/record/1385192002On the range space of Yano’s extrapolation theorem and new extrapolation estimates at infinity
http://ddd.uab.cat/record/138518
Carro, María J.Wed, 30 Sep 2015 11:03:32 GMThttp://ddd.uab.cat/record/1385182002What is van der Corput’s lemma in higher dimensions?
http://ddd.uab.cat/record/138517
We consider variants of van der Corput’s lemma in higher dimensions. Carbery, AnthonyWed, 30 Sep 2015 10:51:42 GMThttp://ddd.uab.cat/record/1385172002