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On Connections Between Hankel, Laguerre and Heisenberg Multipliers
Author(s) -
Stempak Krzysztof
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.2.286
Subject(s) - laguerre polynomials , conjecture , mathematics , hankel transform , pure mathematics , algebra over a field , mathematical analysis , bessel function
We prove two results showing connections between Hankel multipliers, multipliers for a certain kind of Laguerre expansion and multipliers for the Heisenberg sublaplacian. In their spirit they are close to the well‐known theorems of de Leeuw and Igari relating L p multipliers on R and its discrete subgroup Z. Also a conjecture is stated and its consequences are discussed.