ultraspherical expansions
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scholarly journals Discrete Harmonic Analysis Associated with Ultraspherical Expansions

2019 ◽  
Vol 53 (2) ◽  
pp. 523-563 ◽  
Author(s):  
Jorge J. Betancor ◽  
Alejandro J. Castro ◽  
Juan C. Fariña ◽  
L. Rodríguez-Mesa
Keyword(s):  
Harmonic Analysis ◽  
Ultraspherical Expansions

scholarly journals A Hardy Inequality for Ultraspherical Expansions with an Application to the Sphere

2017 ◽  
Vol 24 (2) ◽  
pp. 416-430 ◽  
Author(s):  
Alberto Arenas ◽  
Óscar Ciaurri ◽  
Edgar Labarga
Keyword(s):  
Hardy Inequality ◽  
Ultraspherical Expansions

scholarly journals A choice of Sobolev spaces associated with ultraspherical expansions

2010 ◽  
Vol 54 ◽  
pp. 221-242 ◽  
Author(s):  
J. J. Betancor ◽  
J. C. Fariña ◽  
L. Rodríguez-Mesa ◽  
R. Testoni ◽  
J. L. Torrea
Keyword(s):  
Sobolev Spaces ◽  
Ultraspherical Expansions

scholarly journals Calderón–Zygmund Operators Associated to Ultraspherical Expansions

2007 ◽  
Vol 59 (6) ◽  
pp. 1223-1244 ◽  
Author(s):  
Dariusz Buraczewski ◽  
Teresa Martinez ◽  
José L. Torrea
Keyword(s):  
Differential Operator ◽  
Higher Order ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Type Space ◽  
Ultraspherical Expansions ◽  
Homogeneous Type Space

AbstractWe define the higher order Riesz transforms and the Littlewood–Paley g-function associated to the differential operator Lλf(θ) = –f′′(θ)–2λ cot θ f′(θ) + λ2f(θ). We prove that these operators are Calderón–Zygmund operators in the homogeneous type space ((0, π), (sin t)2λdt). Consequently, Lp weighted, H1 – L1 and L∞ – BMO inequalities are obtained.

HpRepresentation of ultraspherical expansions†

1982 ◽  
Vol 13 (2) ◽  
pp. 139-148 ◽  
Author(s):  
Peter A. Mccoy
Keyword(s):  
Ultraspherical Expansions
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