ISSN:0024-6107    

DOI:10.1112/jlms/49.2.209

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.219

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In the Auslander‐Reiten quiver of a representation‐directed algebra several hammocks occur naturally; they begin at the projective cover of a simple moduleEand end in the corresponding injective hull. It is known that hammocks are Auslander‐Reiten quivers of posets, so there is a poset corresponding to each simple module; it describes the set of modules havingEas a composition factor. In this paper we show that this posetSdecomposes canonically into a coidealS+and an idealS−which can easily be described by vectorspace‐categories corresponding to a one‐point extension or a one‐point coextension, respectively. In addition, we describe the simple modules for whichS+andS−are not comparable, and also those for whichS+⩾S−.We also show how to use the results in order to prove for certain posets that they do not occur as posets corresponding to simple modules.

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.232

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Letw(x),u(x) and υ(x) be weight functions. In this paper, under appropriate conditions on Young's functions Φ1, Φ2we characterize the inequalityΦ2−1(∫0∞Φ2(Tf(x))w(x)dx)⩽Φ1−1(∫0∞Φ1(Cf(x)u(x))υ(x)dx)for the Hardy‐type operatorTdefined in [1] and the inequalityΦ2−1(∫RnΦ2(Mα,υ(fυ)(x))w(x)dv(x))⩽Φ1−1(∫RnΦ1(Cf(x))υ(x)dx)for the fractional maximal operatorMα, υ;defined in [8], as well as the corresponding weak‐type inequalities.

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.244

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We consider the class of transcendental meromorphic functions which have at least one pole and are not conjugate to a self‐map of C∗. We show that the Hausdorff dimension of the Julia set of such a function satisfies 0

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.281

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

For a Calderón‐Zygmund singular integral operatorT, we show that the following weighted inequality holds∫Rn|Tf(y)|pw(y)dy⩽C∫Rn|f(y)|pM[p]+1w(y)dy,whereMkis the Hardy‐Littlewood maximal operatorMiteratedktimes, and [p] is the integer part ofp. Moreover, the result is sharp since it does not hold forM[p]. We also give the following endpoints results:w({y∈Rn:|Tf(y)|>λ})⩽Cλ∫Rn|f(y)|M2w(y)dy,and∫Rn|Tf(y)|w(y)dy⩽C∥f∥H1(Mw),whereH1(μ) is the atomic Hardy space with respect to μ.

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.296

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We examine two related problems concerning a planar domain Ω. The first is whether Sobolev functions on Ω can be approximated by globalC∞functions, and the second is whether approximation can be done by functions inC∞(Ω) which, together with all derivatives, are bounded on Ω. We find necessary and sufficient conditions for certain types of domains, such as starshaped domains, and we construct several examples which show that the general problem is quite difficult, even in the simply connected case.

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.309

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We prove that if a Banach algebra contains an analytic semigroup which satisfies a certain growth condition then neither it nor any homomorphic image of it may have a Strong Wedderburn Decomposition, in particular it must be weakly amenable.

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.331

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.343

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/49.2.357

出版商:Oxford University Press    

年代:2016

数据来源: WILEY