Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
Volume 64 , Issue 4
Showing 1-11 articles out of 11 articles from the selected issue
  • Qingying Xue, Jingquan Yan
    2012 Volume 64 Issue 4 Pages 1053-1069
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    In this paper, we give a natural, and generalized reverse Hölder inequality, which says that if ωiA, then for every cube Q,
    Qmi=1ωiθi ≥ ∏mi=1(∫Qωi/[ωi]A)θi
    where ∑i=1mθi = 1, 0 ≤ θi ≤ 1.
    As a consequence, we get a more general inequality, which can be viewed as an extension of the reverse Jensen inequality in the theory of weighted inequalities. Based on this inequality (0.1), we then give some results concerning multilinear Calderón-Zygmund operators and maximal operators on weighted Hardy spaces, which improve some known results significantly.
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  • Kuniaki Horie, Mitsuko Horie
    2012 Volume 64 Issue 4 Pages 1071-1089
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    Let p be an odd prime, and let B denote the Zp-extension over the rational field. Let l be an odd prime different from p. The question whether the l-class group of B is trivial has been considered in our previous papers mainly for the case where l varies with p fixed. We give a criterion, for checking the triviality of the l-class group of B, which enables us to discuss the triviality when p varies with l fixed. As a consequence, we find that, if l does not exceed 13 and p does not exceed 101, then the l-class group of B is trivial.
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  • Martin T. Barlow, Alexander Grigor'yan, Takashi Kumagai
    2012 Volume 64 Issue 4 Pages 1091-1146
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    We prove the equivalence of parabolic Harnack inequalities and sub-Gaussian heat kernel estimates in a general metric measure space with a local regular Dirichlet form.
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  • Tetsuya Ito
    2012 Volume 64 Issue 4 Pages 1147-1168
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    For an oriented knot K, we construct a functor from the category of pointed quandles to the category of quandles in three different ways. This functor-valued invariant of a knot is an extension of the knot quandle. We also extend the quandle cocycle invariants of knots by using these quandle-valued invariants, and study their properties.
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  • Junjiro Noguchi, Jörg Winkelmann
    2012 Volume 64 Issue 4 Pages 1169-1180
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    Let ι: C2S be a compactification of the two dimensional complex space C2. By making use of Nevanlinna theoretic methods and the classification of compact complex surfaces K. Kodaira proved in 1971 ([2]) that S is a rational surface. Here we deal with a more general meromorphic map f: CnX into a compact complex manifold X of dimension n, whose differential df has generically rank n. Let ρf denote the order of f. We will prove that if ρf < 2, then every global symmetric holomorphic tensor must vanish; in particular, if dim X = 2 and X is kähler, then X is a rational surface. Without the kähler condition there is no such conclusion, as we will show by a counter-example using a Hopf surface. This may be the first instance that the kähler or non-kähler condition makes a difference in the value distribution theory.
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  • Zhen-Qing Chen, Kazuhiro Kuwae
    2012 Volume 64 Issue 4 Pages 1181-1209
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    We establish the equivalence of the analytic and probabilistic notions of subharmonicity in the framework of general symmetric Hunt processes on locally compact separable metric spaces, extending an earlier work of the first named author on the equivalence of the analytic and probabilistic notions of harmonicity. As a corollary, we prove a strong maximum principle for locally bounded finely continuous subharmonic functions in the space of functions locally in the domain of the Dirichlet form under some natural conditions.
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  • Kiryong Chung, Jaehyun Hong, Young-Hoon Kiem
    2012 Volume 64 Issue 4 Pages 1211-1248
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    The space of smooth rational curves of degree d in a projective variety X has compactifications by taking closures in the Hilbert scheme, the moduli space of stable sheaves or the moduli space of stable maps respectively. In this paper we compare these compactifications by explicit blow-ups and -downs when X is a projective homogeneous variety and d ≤ 3. Using the comparison result, we calculate the Betti numbers of the compactifications when X is a Grassmannian variety.
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  • Xiongping Dai
    2012 Volume 64 Issue 4 Pages 1249-1295
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    We study weak hyperbolicity of a differentiable dynamical system which is robustly free of non-hyperbolic periodic orbits of Markus type. Let S be a C1-class vector field on a closed manifold Mn, which is free of any singularities. It is of C1-weak-star in case there exists a C1-neighborhood $¥mathscr{U}$ of S such that for any X ∈ $¥mathscr{U}$, if P is a common periodic orbit of X and S with SP = XP, then P is hyperbolic with respect to X. We show, in the framework of Liao theory, that S possesses the C1-weak-star property if and only if it has a natural and nonuniformly hyperbolic dominated splitting on the set of periodic points Per(S), for the case n = 3.
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  • Makiko Sumi Tanaka, Hiroyuki Tasaki
    2012 Volume 64 Issue 4 Pages 1297-1332
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    We show that the intersections of two real forms, certain totally geodesic Lagrangian submanifolds, in Hermitian symmetric spaces of compact type are antipodal sets. The intersection number of two real forms is invariant under the replacement of the two real forms by congruent ones. If two real forms are congruent, then their intersection is a great antipodal set of them. It implies that any real form in Hermitian symmetric spaces of compact type is a globally tight Lagrangian submanifold. Moreover we describe the intersection of two real forms in the irreducible Hermitian symmetric spaces of compact type.
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  • Kota Yamaura
    2012 Volume 64 Issue 4 Pages 1333-1352
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    In the 1980s, Harada introduced a class of algebras now called Harada algebras. The aim of this paper is to study Harada algebras in representation theoretical point of view. The paper concludes the following two results. The first is the classification of modules over left Harada algebras whose projective dimension is at most one. The second is the classification of tilting modules over left Harada algebras, which is done by giving a bijection between tilting modules over Harada algebras and tilting modules over direct products of upper triangular matrix algebras over a field.
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  • Siegfried Böcherer, Neil Dummigan, Rainer Schulze-Pillot
    2012 Volume 64 Issue 4 Pages 1353-1405
    Published: 2012
    Released: November 16, 2012
    JOURNALS FREE ACCESS
    Let f and g, of weights k′ > k ≥ 2, be normalised newforms for Γ0(N), for square-free N > 1, such that, for each Atkin-Lehner involution, the eigenvalues of f and g are equal. Let λ | ℓ be a large prime divisor of the algebraic part of the near-central critical value L(fg, (k + k′ − 2)/2). Under certain hypotheses, we prove that λ is the modulus of a congruence between the Hecke eigenvalues of a genus-two Yoshida lift of (Jacquet-Langlands correspondents of) f and g (vector-valued in general), and a non-endoscopic genus-two cusp form. In pursuit of this we also give a precise pullback formula for a genus-four Eisenstein series, and a general formula for the Petersson norm of a Yoshida lift.
    Given such a congruence, using the 4-dimensional λ-adic Galois representation attached to a genus-two cusp form, we produce, in an appropriate Selmer group, an element of order λ, as required by the Bloch-Kato conjecture on values of L-functions.
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