On the least values of Lp-norms for the Kontorovich--Lebedev transform and its convolution

  • Authors:

  • Semyon B. Yakubovich

  • Affiliations:

  • Department of Pure Mathematics, Faculty of Sciences, University of Porto, Campo Alegre St., 687, 4169-007 Porto Portugal

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2004

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Abstract

We establish analogs of the Hausdorff-Young and Riesz-Kolmogorov inequalities and the norm estimates for the Kontorovich-Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in L"p spaces, 1=L"p(R"+;xsinh@pxdx),2=