Displaying similar documents to “Embeddings of maximal tori in orthogonal groups”

Spaces with maximal projection constants

Hermann König, Nicole Tomczak-Jaegermann (2003)

Studia Mathematica

Similarity:

We show that n-dimensional spaces with maximal projection constants exist not only as subspaces of l but also as subspaces of l₁. They are characterized by a rigid set of vector conditions. Nevertheless, we show that, in general, there are many non-isometric spaces with maximal projection constants. Several examples are discussed in detail.

A note on rare maximal functions

Paul Alton Hagelstein (2003)

Colloquium Mathematicae

Similarity:

A necessary and sufficient condition is given on the basis of a rare maximal function M l such that M l f L ¹ ( [ 0 , 1 ] ) implies f ∈ L log L([0,1]).

Template iterations and maximal cofinitary groups

Vera Fischer, Asger Törnquist (2015)

Fundamenta Mathematicae

Similarity:

Jörg Brendle (2003) used Hechler’s forcing notion for adding a maximal almost disjoint family along an appropriate template forcing construction to show that (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that g , the minimal size of a maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which enjoys...

Problems on averages and lacunary maximal functions

Andreas Seeger, James Wright (2011)

Banach Center Publications

Similarity:

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to L 1 , bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an L p regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an L p ...

Une inégalité maximale sous-gaussienne sur les espaces de tentes

E. Labeye-Voisin (2003)

Studia Mathematica

Similarity:

We introduce a maximal function (denoted by π̅ ) on the tent spaces T p ( n + 1 ) , 0 < p < ∞, of Coifman, Meyer and Stein [8]. We prove a good-λ estimate of subgaussian type for this maximal function and for the square function of tent spaces, leading to integrability results for π̅. We deduce convergence results for the singular integral defining π.

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

Similarity:

In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

Maximal regularity for second order non-autonomous Cauchy problems

Charles J. K. Batty, Ralph Chill, Sachi Srivastava (2008)

Studia Mathematica

Similarity:

We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has L p -maximal regularity. Then we establish L p -maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).

On the Rademacher maximal function

Mikko Kemppainen (2011)

Studia Mathematica

Similarity:

This paper studies a new maximal operator introduced by Hytönen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The L p -boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to σ-finite measure spaces with filtrations and the L p -boundedness is shown not to depend on the underlying measure space or the filtration. Martingale...

Deformation theory and finite simple quotients of triangle groups I

Michael Larsen, Alexander Lubotzky, Claude Marion (2014)

Journal of the European Mathematical Society

Similarity:

Let 2 a b c with μ = 1 / a + 1 / b + 1 / c < 1 and let T = T a , b , c = x , y , z : x a = y b = z c = x y z = 1 be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of T ? (Classically, for ( a , b , c ) = ( 2 , 3 , 7 ) and more recently also for general ( a , b , c ) .) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially...

Transference and restriction of maximal multiplier operators on Hardy spaces

Zhixin Liu, Shanzhen Lu (1993)

Studia Mathematica

Similarity:

The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces H p ( n ) and H p ( n ) , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an L ( n ) function m is a maximal multiplier on H p ( n ) if and only if it is a maximal multiplier on H p ( n ) . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered. ...

Maximal regularity of discrete and continuous time evolution equations

Sönke Blunck (2001)

Studia Mathematica

Similarity:

We consider the maximal regularity problem for the discrete time evolution equation u n + 1 - T u = f for all n ∈ ℕ₀, u₀ = 0, where T is a bounded operator on a UMD space X. We characterize the discrete maximal regularity of T by two types of conditions: firstly by R-boundedness properties of the discrete time semigroup ( T ) n and of the resolvent R(λ,T), secondly by the maximal regularity of the continuous time evolution equation u’(t) - Au(t) = f(t) for all t > 0, u(0) = 0, where A:= T - I. By recent...

Two results on the Dunkl maximal operator

Luc Deleaval (2011)

Studia Mathematica

Similarity:

In this article, we first improve the scalar maximal theorem for the Dunkl maximal operator by giving some precisions on the behavior of the constants of this theorem for a general reflection group. Next we complete the vector-valued theorem for the Dunkl-type Fefferman-Stein operator in the d case by establishing a result of exponential integrability corresponding to the case p = +∞.

Weak-type inequalities for maximal operators acting on Lorentz spaces

Adam Osękowski (2014)

Banach Center Publications

Similarity:

We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space L p , q , 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant C p , q , r such that for any ϕ L p , q , | | ϕ | | r , C p , q , r | | ϕ | | p , q .

Some remarks on the dyadic Rademacher maximal function

Mikko Kemppainen (2013)

Colloquium Mathematicae

Similarity:

Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) L p inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on ℝⁿ. In addition, to compensate for the lack of an L inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.

Local integrability of strong and iterated maximal functions

Paul Alton Hagelstein (2001)

Studia Mathematica

Similarity:

Let M S denote the strong maximal operator. Let M x and M y denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that Q M y M x h < but Q M x M y h = . It is shown that if f is a function supported on Q such that Q M y M x f < but Q M x M y f = , then there exists a set A of finite measure in ℝ² such that A M S f = .

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

Similarity:

The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age 1 . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....

Symmetry classes of tensors associated with the semi-dihedral groups S D 8 n

Mahdi Hormozi, Kijti Rodtes (2013)

Colloquium Mathematicae

Similarity:

We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups S D 8 n . In particular, a necessary and sufficient condition for the existence of such a basis associated with S D 8 n and degree two characters is given.

The maximal theorem for weighted grand Lebesgue spaces

Alberto Fiorenza, Babita Gupta, Pankaj Jain (2008)

Studia Mathematica

Similarity:

We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality | | M f | | p ) , w c | | f | | p ) , w holds with some c independent of f iff w belongs to the well known Muckenhoupt class A p , and therefore iff | | M f | | p , w c | | f | | p , w for some c independent of f. Some results of similar type are discussed for the case of small...

Maximal operators of Fejér means of double Vilenkin-Fourier series

István Blahota, György Gát, Ushangi Goginava (2007)

Colloquium Mathematicae

Similarity:

The main aim of this paper is to prove that the maximal operator σ * : = s u p | σ n , n | of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space H 1 / 2 to the space weak- L 1 / 2 .

Radial maximal function characterizations for Hardy spaces on RD-spaces

Loukas Grafakos, Liguang Liu, Dachun Yang (2009)

Bulletin de la Société Mathématique de France

Similarity:

An RD-space 𝒳 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type 𝒳 having “dimension” n , there exists a p 0 ( n / ( n + 1 ) , 1 ) such that for certain classes of distributions, the L p ( 𝒳 ) quasi-norms of their radial maximal functions and grand maximal functions are equivalent when p ( p 0 , ] . This result yields a radial maximal function characterization for Hardy spaces on 𝒳 . ...

On the Davenport constant and group algebras

Daniel Smertnig (2010)

Colloquium Mathematicae

Similarity:

For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence S = g · . . . · g l over G such that ( X g - a ) · . . . · ( X g l - a l ) 0 K [ G ] for all a , . . . , a l K × . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for...

A note on the strong maximal operator on ℝⁿ

Jiecheng Chen, Xiangrong Zhu (2004)

Studia Mathematica

Similarity:

We prove that for f ∈ L ln⁺L(ℝⁿ) with compact support, there is a g ∈ L ln⁺L(ℝⁿ) such that (a) g and f are equidistributed, (b) M S ( g ) L ¹ ( E ) for any measurable set E of finite measure.

Sums of commuting operators with maximal regularity

Christian Le Merdy, Arnaud Simard (2001)

Studia Mathematica

Similarity:

Let Y be a Banach space and let S L p be a subspace of an L p space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and be their natural extensions to S ( Y ) L p ( Y ) . We investigate conditions that imply that ℬ + is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and e - t B is a positive contraction...