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The Quarterly Journal of Mathematics Advance Access first published online on June 1, 2008
This version published online on June 5, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han009
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

MIXED WEAK TYPE INEQUALITIES FOR ONE-SIDED OPERATORS

Francisco J. Martín-Reyes{dagger}

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain

Sheldy J. Ombrosi {ddagger}

Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca 8000, Argentina
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain

{dagger} Corresponding author. E-mail: martin_reyes{at}uma.es

Received 22 June 2007; revised 5 March 2008
  Abstract

We discuss mixed weak type inequalities in weighted spaces for one-sided operators. In particular, we prove that if Tcf(x) = (x – c)–1{int}cx f(y) dy, x > c, is the Hardy averaging operator, u isin AFormula (one-sided Muckenhoupt A1 class), and v isin AFormula (another one-sided Muckenhoupt A1 class), then there exists a constant C such that supcisinR {int}{x:|Tcf(x)|>v(x)}uv ≤ C {int}R|f|u.

{ddagger} E-mail: sombrosi{at}uns.edu.ar

The equation on line -4 of page 2 has been corrected.


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