1,711 research outputs found
On radial Fourier multipliers and almost everywhere convergence
We study a.e. convergence on , and Lorentz spaces ,
, for variants of Riesz means at the critical index
. We derive more general results for
(quasi-)radial Fourier multipliers and associated maximal functions, acting on
spaces with power weights, and their interpolation spaces. We also
include a characterization of boundedness of such multiplier transformations on
weighted spaces, and a sharp endpoint bound for Stein's square-function
associated with the Riesz means
Endpoint bounds of square functions associated with Hankel multipliers
We prove endpoint bounds for the square function associated with radial
Fourier multipliers acting on radial functions. This is a consequence
of endpoint bounds for a corresponding square function for Hankel multipliers.
We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel
multipliers and bounds of maximal operators generated by Hankel
multipliers as corollaries. The proof is built on techniques developed by
Garrig\'{o}s and Seeger for characterizations of Hankel multipliers.Comment: 26 page
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