Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Rearrangement of Hardy-Littlewood maximal functions in Lorentz spaces

Authors:	Jesú s Bastero Mario Milman Francisco J. Ruiz

Affiliation:	Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain ; Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431 ; Department of Mathematics, University of Zaragoza, 50009-Zaragoza, Spain

Abstract:	For the classical Hardy-Littlewood maximal function , 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 $begin{equation}M_{p,q}f(x)= sup _{xin Q}{frac{Vert fchi _{Q} Vert _{p,q} }{Vert chi _{Q} Vert _{p,q}}}, end{equation*}$ where $Vert . Vert _{p,q}$ denotes the Lorentz space -norm.

Keywords:	Maximal functions rearrangement inequalities Lorentz spaces

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