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  • Articles  (1,169)
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  • Oxford University Press  (1,169)
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  • 1
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    ON FEFFERMAN-STEIN INEQUALITY FOR RUBIO DE FRANCIA OPERATORS (2012)
    Oxford University Press
    Details
    Publication Date: 2012-02-14
    Description: Given a Calderón–Zygmund singular integral operator, it is an open question whether the Fefferman inequality holds true with u as an arbitrary weight. This inequality is known as the Muckenhoupt–Wheeden conjecture. In this paper we prove that, for a wider class of operators called Rubio de Francia operators, if || u || ≤1, then where the function is slightly bigger than the identity. Applications of this inequality in the setting of rearrangement invariant spaces are given.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    TRUNCATED SIMPLICIAL RESOLUTIONS AND SPACES OF RATIONAL MAPS (2012)
    Oxford University Press
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    Publication Date: 2012-02-14
    Description: We show that whenever m ≤ n , the space of all continuous rational maps from CP m to CP n has the same homology as the space of all continuous maps between these spaces in dimensions smaller than d (2 n – 2 m + 1) – 1. This improves the result of the paper ‘Spaces of rational maps and the Stone–Weierstrass theorem’ ( Topology 45 (2006), 281–293).
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    Topics: Mathematics
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  • 3
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    EXACT COVERING SYSTEMS IN QUADRATIC NUMBER FIELDS (2012)
    Oxford University Press
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    Publication Date: 2012-02-14
    Description: A theorem of Davenport, Mirsky, Newman and Rado shows that there does not exist an exact covering system with distinct moduli. Motivated by this, we raise the question whether or not this is true for covering systems in algebraic number fields. We provide an affirmative answer for certain quadratic fields.
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    Topics: Mathematics
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  • 4
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    CAUSTICS OF SURFACES IN THE MINKOWSKI 3-SPACE (2012)
    Oxford University Press
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    Publication Date: 2012-02-14
    Description: The caustic of a smooth surface in the Euclidean 3-space is the envelope of the normal rays to the surface. It is also the locus of the centres of curvature (the focal points) of the surface. This is why it is also referred to as the focal set of the surface. It has Lagrangian singularities and its generic models are given in [V. I. Arnol’d, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps , Vol. I, Birkhäuser, Boston, 1986]. The aim of this paper is to define the caustic C ( M ) of a smooth surface M embedded in the Minkowski 3-space and to study its geometry. We denote by the locus of degeneracy (LD) the locus of points on M where the metric is degenerate. If M is a closed surface then its LD is not empty. At a point on the LD the ‘normal’ line to M is lightlike and is tangent to M . Also, the focal set of M is not defined at points on the LD. We define the caustic of M as the bifurcation set of the family of distance-squared functions on M . Then C ( M ) coincides with the focal set of M \ LD and provides an extension of the focal set to the LD. We study the local behaviour of the metric on C ( M ).
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    Topics: Mathematics
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  • 5
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    LIE POWERS OF THE NATURAL MODULE FOR GL(2,K) (2013)
    Oxford University Press
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    Publication Date: 2013-02-20
    Description: In a recent work of R. M. Bryant and the second author, a (partial) modular analogue of Klyachko's 1974 result on Lie powers of the natural module for GL( n , K ) was presented. There it was shown that nearly all of the indecomposable summands of the r th tensor power also occur up to isomorphism as summands of the r th Lie power, provided that r != p m and r !=2 p m , where p is the characteristic of K . In the current paper, we restrict attention to GL(2, K ) and consider the missing cases where r = p m and r =2 p m . In particular, we prove that the indecomposable summand of the r th tensor power of the natural module with highest weight ( r –1, 1) is a summand of the r th Lie power if and only if r = p or r is not a power of p .
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    Topics: Mathematics
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  • 6
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    THE SOBOLEV NORM OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS TO THE CALDERON INVERSE PROBLEM (2013)
    Oxford University Press
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    Publication Date: 2013-02-20
    Description: We consider Calderón's inverse problem on planar domains with conductivities in fractional Sobolev spaces. When is Lipschitz, the problem was shown to be stable in the L 2 -sense in Clop et al. [Stability of calderón's inverse conductivity problem in the plane for discontinuous conductivities, Inverse Probl. Imaging 4 (2010), 49–91]. We remove the Lipschitz condition on the boundary. To this end, we analyse the Sobolev regularity of the characteristic function of . For a quasiball, we compute || || W s , p (R d ) in terms of the -neighbourhoods of the boundary.
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    Topics: Mathematics
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  • 7
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    ON CERTAIN 5-MANIFOLDS WITH FUNDAMENTAL GROUP OF ORDER 2 (2013)
    Oxford University Press
    Details
    Publication Date: 2013-02-20
    Description: In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply connected 4-manifolds.
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    Topics: Mathematics
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  • 8
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    POWER-FREE VALUES OF POLYNOMIALS (2013)
    Oxford University Press
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    Publication Date: 2013-02-20
    Description: For irreducible polynomials of the form X d + c we establish the expected asymptotic formula for the number of k -free integers n d + c with n ≤ x , under the assumption that k ≥ (5 d + 3)/9. Previous techniques required k 〉 3 d /4. We also prove an entirely analogous result for p d + c with p prime.
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    Topics: Mathematics
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  • 9
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    ON THE J-ANTI-INVARIANT COHOMOLOGY OF ALMOST COMPLEX 4-MANIFOLDS (2013)
    Oxford University Press
    Details
    Publication Date: 2013-02-20
    Description: For a compact almost complex 4-manifold ( M , J ), we study the subgroups H ± J of H 2 ( M , R) consisting of cohomology classes representable by J -invariant, respectively, J -anti-invariant real 2-forms. If b + =1, we show that, for generic almost complex structures on M , the subgroup H – J is trivial. Computations of the subgroups and their dimensions h ± J are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for h ± J .
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    Topics: Mathematics
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  • 10
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    LOOP GROUPS AND HOLOMORPHIC BUNDLES (2013)
    Oxford University Press
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    Publication Date: 2013-02-20
    Description: This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. A topological stability result for the moduli on a rational ruled surface of G -bundles with additional flag structure along a line is proved for any reductive group; this gives the corresponding stability statement for any compact group K for the moduli of K -instantons over the four-sphere, and for the moduli of K -calorons over R 3 times the circle.
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    Topics: Mathematics
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