• Title/Summary/Keyword: uniform spaces

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A VAN DER CORPUT TYPE LEMMA FOR OSCILLATORY INTEGRALS WITH HÖLDER AMPLITUDES AND ITS APPLICATIONS

  • Al-Qassem, Hussain;Cheng, Leslie;Pan, Yibiao
    • Journal of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.487-499
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    • 2021
  • We prove a decay estimate for oscillatory integrals with Hölder amplitudes and polynomial phases. The estimate allows us to answer certain questions concerning the uniform boundedness of oscillatory singular integrals on various spaces.

GEOMETRY ON EXOTIC HYPERBOLIC SPACES

  • Kim, In-Kang
    • Journal of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.621-631
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    • 1999
  • In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

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U-FLATNESS AND NON-EXPANSIVE MAPPINGS IN BANACH SPACES

  • Gao, Ji;Saejung, Satit
    • Journal of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.493-506
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    • 2017
  • In this paper, we define the modulus of n-dimensional U-flatness as the determinant of an $(n+1){\times}(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.

BARRELLEDNESS OF SOME SPACES OF VECTOR MEASURES AND BOUNDED LINEAR OPERATORS

  • FERRANDO, JUAN CARLOS
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1579-1586
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    • 2015
  • In this paper we investigate the barrellednes of some spaces of X-valued measures, X being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space X into a barrelled normed space Y, equipped with the uniform convergence topology.