Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions

Authors:
Natan Kruglyak and Eric Setterqvist

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2505-2513

MSC (2000):
Primary 26D10, 46E30

DOI:
https://doi.org/10.1090/S0002-9939-08-09200-9

Published electronically:
March 7, 2008

MathSciNet review:
2390520

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions in , then we have the sharp estimate

It is also shown, via a connection between the operator and Laguerre functions, that

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Additional Information

**Natan Kruglyak**

Affiliation:
Department of Mathematics, Luleå University of Technology, SE-971 87, Luleå, Sweden

Email:
natan@ltu.se

**Eric Setterqvist**

Affiliation:
Global Sun Engineering AB, Aurorum Science Park 2, SE-97775 Luleå, Sweden

Email:
eric.setterquist@globalsunengineering.com

DOI:
https://doi.org/10.1090/S0002-9939-08-09200-9

Keywords:
The Hardy operator,
cone of decreasing functions,
sharp estimates

Received by editor(s):
February 9, 2006

Received by editor(s) in revised form:
January 26, 2007, and March 30, 2007

Published electronically:
March 7, 2008

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2008
American Mathematical Society