Hankel Multipliers And Transplantation Operators

Connections between Hankel transforms of different order for $L^p$-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated

On a restriction problem of de Leeuw type for Laguerre multipliers

In 1965 K. de Leeuw \cite{deleeuw} proved among other things in the Fourier transform setting: {\it If a continuous function $m(\xi _1, \ldots ,\xi _n)$ on ${\bf R}^n$ generates a bounded transformation on $L^p({\bf R}^n),\; 1\le p \le \infty ,$ then its trace $\tilde{m}(\xi _1, \ldots ,\xi _m)=m(\xi _1, \ldots ,\xi _m,0,\ldots ,0), \; m<n,$ generates a bounded transformation on $L^p({\bf R}^m)$. } In this paper, the analogous problem is discussed in the setting of Laguerre expansions of different orders

Ultraspherical multipliers revisited

Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen type inequalities. Muckenhoupt's transplantation theorem is used in an essential way