Ultraspherical multipliers revisited
George Gasper Jr, Walter Trebels
TL;DR
This paper refines ultraspherical multiplier criteria to align with necessary conditions and introduces new necessary conditions for Jacobi multipliers, utilizing Muckenhoupt's transplantation theorem.
Contribution
It provides improved ultraspherical multiplier criteria and new necessary conditions for Jacobi multipliers, advancing the theoretical understanding of these operators.
Findings
Refined ultraspherical multiplier criteria comparable with necessary conditions.
New necessary conditions for Jacobi multipliers.
Implications for Cohen type inequalities.
Abstract
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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Advanced Banach Space Theory