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2 results

  • Vector-valued Hausdorff–Young inequality on compact groups

  • J. García-Cuerva, J. Parcet
  • Journal:
    Proceedings of the London Mathematical Society / Volume 88 / Issue 3 / May 2004
    Published online by Cambridge University Press:
    14 April 2004, pp. 796-816
    Print publication:
    May 2004

  • The main purpose of this paper is to study the validity of the Hausdorff–Young inequality for vector-valued functions defined on a non-commutative compact group. As we explain in the introduction, the natural context for this research is that of operator spaces. This leads us to formulate a whole new theory of Fourier type and cotype for the category of operator spaces. The present paper is the first step in this program, where the basic theory is presented, the main examples are analyzed and some important questions are posed.

  • Uniform saddlepoint approximations

  • J. L. Jensen
  • Journal:
    Advances in Applied Probability / Volume 20 / Issue 3 / September 1988
    Published online by Cambridge University Press:
    01 July 2016, pp. 622-634
    Print publication:
    September 1988

  • The validity of the saddlepoint expansion evaluated at the point y is considered in the limit y tending to ∞. This is done for the expansions of the density and of the tail probability of the mean of n i.i.d. random variables and also for the expansion of the tail probability of a compound Poisson sum , where N is a Poisson random variable. We consider both general conditions that ensure the validity of the expansions and study the four classes of densities for X1 introduced in Daniels (1954).