scholarly journals H1-boundedness of Riesz transforms and imaginary powers of the Laplacian on Riemannian manifolds

2003 ◽  
Vol 41 (1) ◽  
pp. 115-132 ◽  
Author(s):  
Michel Marias ◽  
Emmanuel Russ
Keyword(s):  
Riemannian Manifolds ◽  
Riesz Transforms ◽  
Imaginary Powers

scholarly journals Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

2011 ◽  
Vol 61 (4) ◽  
pp. 1323-1349 ◽  
Author(s):  
Steve Hofmann ◽  
Marius Mitrea ◽  
Sylvie Monniaux
Keyword(s):  
Riemannian Manifolds ◽  
Riesz Transforms ◽  
Hodge Laplacian

scholarly journals Higher-Order Riesz Transforms in the Inverse Gaussian Setting and UMD Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-28
Author(s):  
Jorge J. Betancor ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Banach Spaces ◽  
Gaussian Measure ◽  
Singular Integrals ◽  
Higher Order ◽  
Riesz Transforms ◽  
Inverse Gaussian ◽  
Imaginary Powers ◽  
Umd Banach Spaces

In this paper, we study higher-order Riesz transforms associated with the inverse Gaussian measure given by π n / 2 e x 2 d x on ℝ n . We establish L p ℝ n , e x 2 d x -boundedness properties and obtain representations as principal values singular integrals for the higher-order Riesz transforms. New characterizations of the Banach spaces having the UMD property by means of the Riesz transforms and imaginary powers of the operator involved in the inverse Gaussian setting are given.

scholarly journals Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds

2014 ◽  
Vol 224 (2) ◽  
pp. 153-168 ◽  
Author(s):  
Giancarlo Mauceri ◽  
Stefano Meda ◽  
Maria Vallarino
Keyword(s):  
Riesz Transforms ◽  
Noncompact Manifolds ◽  
Imaginary Powers

scholarly journals Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds

2007 ◽  
Vol 344 (2) ◽  
pp. 103-108 ◽  
Author(s):  
Pascal Auscher ◽  
Alan McIntosh ◽  
Emmanuel Russ
Keyword(s):  
Riemannian Manifolds ◽  
Hardy Spaces ◽  
Differential Forms ◽  
Riesz Transforms
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