Displaying similar documents to “A maximal function on harmonic extensions of H -type groups”

A.e. convergence of spectral sums on Lie groups

Christopher Meaney, Detlef Müller, Elena Prestini (2007)

Annales de l’institut Fourier

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Let be a right-invariant sub-Laplacian on a connected Lie group G , and let S R f : = 0 R d E λ f , R 0 , denote the associated “spherical partial sums,” where = 0 λ d E λ is the spectral resolution of . We prove that S R f ( x ) converges a.e. to f ( x ) as R under the assumption log ( 2 + ) f L 2 ( G ) .

Approximation of values of hypergeometric functions by restricted rationals

Carsten Elsner, Takao Komatsu, Iekata Shiokawa (2007)

Journal de Théorie des Nombres de Bordeaux

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We compute upper and lower bounds for the approximation of hyperbolic functions at points 1 / s ( s = 1 , 2 , ) by rationals x / y , such that x , y satisfy a quadratic equation. For instance, all positive integers x , y with y 0 ( mod 2 ) solving the Pythagorean equation x 2 + y 2 = z 2 satisfy | y sinh ( 1 / s ) - x | log log y log y . Conversely, for every s = 1 , 2 , there are infinitely many coprime integers x , y , such that | y sinh ( 1 / s ) - x | log log y log y and x 2 + y 2 = z 2 hold simultaneously for some integer z . A generalization to the approximation of h ( e 1 / s ) for rational...

Necessary condition for measures which are ( L q , L p ) multipliers

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2009)

Annales mathématiques Blaise Pascal

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Let G be a locally compact group and ρ the left Haar measure on G . Given a non-negative Radon measure μ , we establish a necessary condition on the pairs q , p for which μ is a multiplier from L q G , ρ to L p G , ρ . Applied to n , our result is stronger than the necessary condition established by Oberlin in [14] and is closely related to a class of measures defined by Fofana in [7]. When G ...

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n x n on n is proved. In this note there is shown that in the cases k 0 , k 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.