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Volume 28 - 01 June 1985

Contents

Page 4 of 4

Research Article

  • A Reflexive LUR Banach Space that Lacks Normal Structure

  • Mark A. Smith, Barry Turett
  • Published online by Cambridge University Press:
    20 November 2018, pp. 492-494
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  • An example of the type described in the title is given.

  • Cauchy Integral of Calderón on the Graphs of Functions with BMO Derivatives

  • Kôzô Yabuta
  • Published online by Cambridge University Press:
    20 November 2018, pp. 495-500
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  • We first note that each graph (x,A(x)) of a function A(x) with BMO derivative is a chord-arc curve. Using this, Muckenhoupt's Ap theory, and the theory of Calderón-Zygmund operators, we shall derive weighted norm inequalities for the Cauchy integral on such graphs from a recent theorem of G. David on the L2-boundedness of Cauchy integral on almost-lipschitzian curves.

  • Certain Values of Completeness and Saturatedness of a Uniform Ideal Rule out Certain Sizes of The Underlying Index Set

  • Frantisek Franek
  • Published online by Cambridge University Press:
    20 November 2018, pp. 501-504
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  • Using the method of non-well-founded generic ultra-powers, we shall prove a generalization of a theorem of Taylor that certain values of completeness and saturatedness of a uniform ideal rule out certain sizes of the underlying index set.

  • The Definability of the Commutator Subgroup in a Variety Generated by a Finite Group

  • John Lawrence
  • Published online by Cambridge University Press:
    20 November 2018, pp. 505-507
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  • In a variety generated by a finite non-Abelian group, the commutator subgroup is not definable by a first-order formula.

Page 4 of 4