Lorentz-Zygmund Spaces and Interpolation of Weak Type Operators

Author: Rudnick, Karl Hansell

Year: 1976

Degree: Dissertation (Ph.D.)

Advisor: Bennett, Colin

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/7TM3-QK38

Abstract

The Lorentz-Zygmund spaces L^pa(log L)^α are a class of function spaces containing as special cases the classical Lebesgue spaces L^p, the Lorentz spaces L^pa and the Zygmund spaces L^p(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.

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