Local integrability of strong and iterated maximal functions

• Autorzy: Paul Alton Hagelstein
• Języki publikacji: EN

Abstrakty

EN

Let $M_{S}$ denote the strong maximal operator. Let $M_{x}$ and $M_{y}$ denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that $∫_{Q} M_{y}M_{x}h < ∞$ but $∫_{Q} M_{x}M_{y}h = ∞$. It is shown that if f is a function supported on Q such that $∫_{Q} M_{y}M_{x}f < ∞$ but $∫_{Q} M_{x}M_{y}f = ∞$, then there exists a set A of finite measure in ℝ² such that $∫_{A} M_{S}f = ∞$.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 1
• Strony: 37-50

Daty

wydano

2001

Twórcy

autor

Paul Alton Hagelstein

• Department of Mathematics, Princeton University, Princeton, NJ 08544, U.S.A.

Identyfikatory

DOI

10.4064/sm147-1-4