Volume 4,  Issue 4, 2003

Article 81

WEIGHTED WEAK TYPE INEQUALITIES FOR THE HARDY OPERATOR WHEN p=1

TIELING CHEN

MATHEMATICAL SCIENCES DEPARTMENT
UNIVERSITY OF SOUTH CAROLINA AIKEN
471 UNIVERSITY PARKWAY
AIKEN, SC 29801, USA.


E-Mail: tielingc@usca.edu

Received 23 June, 2003; Accepted 22 September, 2003.
Communicated by: T. Mills


ABSTRACT.    The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted $ L^p$ to weighted weak $ L^q$ in the case $ p = 1$. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when $ p = 1$. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when $ q<p=1$. The best constant in the inequality is also estimated.
Key words:
Hardy operator, Weak type inequality.

2000 Mathematics Subject Classification:
26D15.


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