Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces
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- by Jesús Bastero, Mario Milman and Francisco J. Ruiz PDF
- Proc. Amer. Math. Soc. 128 (2000), 65-74 Request permission
Abstract:
For the classical Hardy-Littlewood maximal function $Mf$, a well known and important estimate due to Herz and Stein gives the equivalence $(Mf)^{*}(t)\sim f^{**}(t)$. In the present note, we study the validity of analogous estimates for maximal operators of the form \begin{equation*}M_{p,q}f(x)= \sup _{x\in Q}{\frac {\Vert f\chi _{Q} \Vert _{p,q} }{\Vert \chi _{Q} \Vert _{p,q}}}, \end{equation*} where $\Vert . \Vert _{p,q}$ denotes the Lorentz space $L(p,q)$-norm.References
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Additional Information
- Jesús Bastero
- Affiliation: Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain
- Email: bastero@posta.unizar.es
- Mario Milman
- Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
- Email: milman@acc.fau.edu
- Francisco J. Ruiz
- Affiliation: Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain
- Email: fjruiz@posta.unizar.es
- Received by editor(s): March 2, 1998
- Published electronically: June 30, 1999
- Additional Notes: The first author was partially supported by DGICYT PB94-1185.
The third author was partially supported by DGICYT and IER - Communicated by: Frederick W. Gehring
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 65-74
- MSC (1991): Primary 42B25, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-99-05128-X
- MathSciNet review: 1641637