This paper is concerned with inequalities of the form ∥Ax∥q ≤ C∥x∥p, where A and x are infinite versions of square and column matrices, respectively, C is independent of x, and the norms are the standard ones in ℓq and l p. While special inequalities of this kind have received extensive attention long ago, relatively little work seems to have appeared until recently with general matrices A such as are discussed here. An application to certain summability matrices is added.


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Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • E. R. Love
    • 1
  1. 1.Department of MathematicsUniversity of MelbourneParkvilleAustralia

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