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 to weighted weak in the case . It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when . It proves that for the classical Hardy operator, the weak type inequality is generally weaker when . 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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