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March, 2004 Endpoint estimates from restricted rearrangement inequalities
María J. Carro, Joaquim Martín
Rev. Mat. Iberoamericana 20(1): 131-150 (March, 2004).

Abstract

Let $T$ be a sublinear operator such that $(Tf)^*(t)\le h(t, \|f\|_1)$ for some positive function $h(t,s)$ and every function $f$ such that $\|f\|_{\infty}\le 1$. Then, we show that $T$ can be extended continuously from a logarithmic type space into a weighted weak Lorentz space. This type of result is connected with the theory of restricted weak type extrapolation and extends a recent result of Arias-de-Reyna concerning the pointwise convergence of Fourier series to a much more general context.

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María J. Carro. Joaquim Martín. "Endpoint estimates from restricted rearrangement inequalities." Rev. Mat. Iberoamericana 20 (1) 131 - 150, March, 2004.

Information

Published: March, 2004
First available in Project Euclid: 2 April 2004

zbMATH: 1063.46061
MathSciNet: MR2076775

Subjects:
Primary: 46M35 , 47A30

Keywords: Banach couples , Carleson's operator , extrapolation theory , real interpolation , rearrangement inequality

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.20 • No. 1 • March, 2004
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