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Lorentz-Zygmund Spaces and Interpolation of Weak Type Operators


Rudnick, Karl Hansell (1976) Lorentz-Zygmund Spaces and Interpolation of Weak Type Operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7TM3-QK38.


The Lorentz-Zygmund spaces Lpa(log L)α are a class of function spaces containing as special cases the classical Lebesgue spaces Lp, the Lorentz spaces Lpa and the Zygmund spaces Lp(log L)α. It is shown here that the Lorentz-Zygmund spaces provide the correct framework for the interpolation theory of weak type operators. The interpolation principles established here unify many classical results in harmonic analysis. In particular, there are applications to the Fourier transform, the Hardy-Littlewood maximal operator, the Hilbert transform, and the Weyl fractional integrals.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bennett, Colin
Thesis Committee:
  • Unknown, Unknown
Defense Date:20 May 1976
Funding AgencyGrant Number
Record Number:CaltechTHESIS:02222017-144637159
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10061
Deposited By: Benjamin Perez
Deposited On:22 Feb 2017 23:40
Last Modified:09 Nov 2022 19:20

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