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2 results

  • Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities

  • Joseph D. Lakey
  • Journal:
    Canadian Journal of Mathematics / Volume 46 / Issue 3 / 01 June 1994
    Published online by Cambridge University Press:
    20 November 2018, pp. 586-601
    Print publication:
    01 June 1994
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  • Wiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates

  • Weighted Restriction for Curves

  • Joseph D. Lakey
  • Journal:
    Canadian Mathematical Bulletin / Volume 36 / Issue 1 / 01 March 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 87-95
    Print publication:
    01 March 1993
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  • We prove weighted norm inequalities for the Fourier transform of the form

    where v is a nonnegative weight function on ℝd and ψ: [— 1,1 ] —> ℝd is a nondegenerate curve. Our results generalize unweighted (i.e. v = 1) restriction theorems of M. Christ, and two-dimensional weighted restriction theorems of C. Carton-Lebrun and H. Heinig.