Tohoku Mathematical Journal
2006
June
SECOND SERIES VOL. 58, NO. 2

Tohoku Math. J.
58 (2006), 277-301

Title WEIGHTED ESTIMATES FOR THE HANKEL TRANSFORM TRANSPLANTATION OPERATOR

Author Adam Nowak and Krzysztof Stempak

(Received July 13, 2004, revised April 25, 2005)
Abstract. The Hankel transform transplantation operator is investigated by means of a suitably established local version of the Calderón-Zygmund operator theory. This approach produces weighted norm inequalities with weights more general than previously considered power weights. Moreover, it also allows to obtain weighted weak type $(1,1)$ inequalities, which seem to be new even in the unweighted setting. As a typical application of the transplantation, multiplier results in weighted $L^p$ spaces with general weights are obtained for the Hankel transform of any order greater than $-1$ by transplanting cosine transform multiplier results.

2000 Mathematics Subject Classification. Primary 42C10; Secondary 44A20.
Key words and phrases. Hankel transform, transplantation, weighted norm inequalities, weighted weak type inequalities, local Calderón-Zygmund operators, local $A_p$ weights, multipliers.

To the top of this page

Back to the Contents