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On extrapolation blowups in the scale

Abstract

Yano's extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator acting continuously in for close to and/or taking into as and/or with norms blowing up at speed and/or,. Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if as. The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for . We also touch the problem of comparison of results in various scales of spaces.

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Correspondence to Claudia Capone.

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Capone, C., Fiorenza, A. & Krbec, M. On extrapolation blowups in the scale. J Inequal Appl 2006, 74960 (2006). https://doi.org/10.1155/JIA/2006/74960

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Keywords

  • Current Investigation
  • Maximal Function
  • Lebesgue Space
  • Stochastic Analysis
  • Boundedness Property
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