Bochner-Riesz means with negative index of radial functions in Sobolev spaces

1993 ◽  
Vol 42 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Luca Brandolini ◽  
Leonardo Colzani
Keyword(s):  
Sobolev Spaces ◽  
Negative Index ◽  
Riesz Means ◽  
Radial Functions

scholarly journals GLOBAL WELL-POSEDNESS OF THE 1D DIRAC–KLEIN–GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX

2009 ◽  
Vol 06 (03) ◽  
pp. 631-661 ◽  
Author(s):  
ACHENEF TESFAHUN
Keyword(s):  
Sobolev Spaces ◽  
Well Posedness ◽  
Dirac Spinor ◽  
Negative Index ◽  
Main Ingredient ◽  
Time Estimates ◽  
The Cauchy Problem ◽  
Klein Gordon ◽  
Positive Index ◽  
Well Posed

We prove that the Cauchy problem for the Dirac–Klein–Gordon system of equations in 1D is globally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor and positive index for the scalar field. The main ingredient in the proof is the theory of "almost conservation law" and "I-method" introduced by Colliander, Keel, Staffilani, Takaoka, and Tao. Our proof also relies on the null structure in the system, and bilinear space–time estimates of Klainerman–Machedon type.

scholarly journals Approximation numbers of Sobolev embeddings of radial functions on isotropic manifolds

2007 ◽  
Vol 5 (1) ◽  
pp. 27-48 ◽  
Author(s):  
Leszek Skrzypczak ◽  
Bernadeta Tomasz
Keyword(s):  
Asymptotic Formula ◽  
Sobolev Spaces ◽  
Symmetric Spaces ◽  
Approximation Numbers ◽  
Radial Functions ◽  
Sobolev Embeddings ◽  
Rank One

We regard the compact Sobolev embeddings between Besov and Sobolev spaces of radial functions on noncompact symmetric spaces of rank one. The asymptotic formula for the behaviour of approximation numbers of these embeddings is described.

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