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Radial maximal function characterizations for Hardy spaces on RD-spaces

Loukas Grafakos, Liguang Liu, Dachun Yang (2009)

Bulletin de la Société Mathématique de France

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 .

Random walks on free products

M. Gabriella Kuhn (1991)

Annales de l'institut Fourier

Let G = * j = 1 q + 1 G n j + 1 be the product of q + 1 finite groups each having order n j + 1 and let μ be the probability measure which takes the value p j / n j on each element of G n j + 1 { e } . In this paper we shall describe the point spectrum of μ in C reg * ( G ) and the corresponding eigenspaces. In particular we shall see that the point spectrum occurs only for suitable choices of the numbers n j . We also compute the continuous spectrum of μ in C reg * ( G ) in several cases. A family of irreducible representations of G , parametrized on the continuous spectrum of μ ,...

Range inclusion results for derivations on noncommutative Banach algebras

Volker Runde (1993)

Studia Mathematica

Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...

Rank α operators on the space C(T,X)

Dumitru Popa (2002)

Colloquium Mathematicae

For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if x τ α x implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.

Real-linear isometries between certain subspaces of continuous functions

Arya Jamshidi, Fereshteh Sady (2013)

Open Mathematics

In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin...

Recent developments in the theory of function spaces with dominating mixed smoothness

Schmeisser, Hans-Jürgen (2007)

Nonlinear Analysis, Function Spaces and Applications

The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...

Recovery of band-limited functions on locally compact Abelian groups from irregular samples

H. G. Feichtinger, S. S. Pandey (2003)

Czechoslovak Mathematical Journal

Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group G . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative...

Recurrence and mixing recurrence of multiplication operators

Mohamed Amouch, Hamza Lakrimi (2024)

Mathematica Bohemica

Let X be a Banach space, ( X ) the algebra of bounded linear operators on X and ( J , · J ) an admissible Banach ideal of ( X ) . For T ( X ) , let L J , T and R J , T ( J ) denote the left and right multiplication defined by L J , T ( A ) = T A and R J , T ( A ) = A T , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between T ( X ) , and their elementary operators L J , T and R J , T . In particular, we give necessary and sufficient conditions for L J , T and R J , T to be sequentially recurrent. Furthermore, we prove that L J , T is recurrent if and only...

Reduced Cowen sets.

Curto, Raúl E., Lee, Woo Young (2001)

The New York Journal of Mathematics [electronic only]

Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space

Yong Chen, Young Joo Lee, Tao Yu (2014)

Studia Mathematica

We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if...

Reducible representations of abelian groups

Aharon Atzmon (2001)

Annales de l’institut Fourier

A criterion for reducibility of certain representations of abelian groups is established. Among the applications of this criterion, we give a positive answer to the translation invariant subspace problem for weighted L p spaces on locally compact abelian groups, for even weights and 1 &lt; p &lt; .

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