On weighted transplantation and multipliers for Laguerre expansions

Details On weighted transplantation and multipliers for Laguerre expansions On weighted transplantation and multipliers for Laguerre expansions

1993-07-08

arxiv.org/abs/math/9307203v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Using the standard square--function method (based on the Poisson semigroup), multiplier conditions of H\"ormander type are derived for Laguerre expansions in $L^p$--spaces with power weights in the $A_p$-range; this result can be interpreted as an ``upper end point'' multiplier criterion which is fairly good for $p$ near $1$ or near $\infty $. A weighted generalization of Kanjin's \cite{kan} transplantation theorem allows to obtain a ``lower end point'' multiplier criterion whence by interpolation nearly ``optimal'' multiplier criteria (in dependance of $p$, the order of the Laguerre polynomial, the weight).

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