Characterizations of Hankel multipliers
نویسندگان
چکیده
منابع مشابه
Characterizations of Hankel Multipliers
We give characterizations of radial Fourier multipliers as acting on radial L functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L −L bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces....
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Connections between Hankel transforms of different order for L-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.
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Let Hμ be the Zemanian space of Hankel transformable functions, and let H′μ be its dual space. In this paper Hμ is shown to be nuclear, hence Schwartz, Montel and reflexive. The space O, also introduced by Zemanian, is completely characterized as the set of multipliers of Hμ and of H′μ. Certain topologies are considered on O, and continuity properties of the multiplication operation with respec...
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An example of a polynomially bounded operator on Hilbert space not similar to a contraction was found recently by Pisier [Pi]. An operatortheoretic proof that certain CAR-valued Foguel-Hankel operators are polynomially bounded operators but not similar to contractions was given by Davidson and Paulsen [DP]. It is still an open question [DP] to characterize operators in this family which are sim...
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Let m have compact support in (0,∞). For 1 < p < 2d/(d + 1), we give a necessary and sufficient condition for the Lprad(R )-boundedness of the maximal operator associated with the radial multiplier m(|ξ|). More generally we prove a similar result for maximal operators associated with multipliers of modified Hankel transforms. The result is obtained by modifying the proof of the characterization...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2008
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-008-0221-8