scholarly journals Higher order Riesz transforms for Laguerre expansions

2011 ◽  
Vol 55 (1) ◽  
pp. 27-68 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan C. Fariña ◽  
Lourdes Rodríguez-Mesa ◽  
Alejandro Sanabria-García
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Laguerre Expansions

scholarly journals Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions

2005 ◽  
Vol 84 (3) ◽  
pp. 375-405 ◽  
Author(s):  
Piotr Graczyk ◽  
Jean-J. Loeb ◽  
Iris A. López P. ◽  
Adam Nowak ◽  
Wilfredo O. Urbina R.
Keyword(s):  
Sobolev Spaces ◽  
Fractional Derivatives ◽  
Higher Order ◽  
Riesz Transforms ◽  
Laguerre Expansions

scholarly journals Riesz Transforms Associated with Higher-Order Schrödinger Type Operators

2017 ◽  
Vol 49 (3) ◽  
pp. 381-410
Author(s):  
Qingquan Deng ◽  
Yong Ding ◽  
Xiaohua Yao
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Schrödinger Type Operators

scholarly journals Higher order Riesz transforms associated with Bessel operators

2008 ◽  
Vol 46 (2) ◽  
pp. 219-250 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan C. Fariña ◽  
Teresa Martinez ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Bessel Operators

Riesz transforms and g-function for Laguerre expansions

2006 ◽  
Vol 55 (3) ◽  
pp. 999-1014 ◽  
Author(s):  
E. Harboure ◽  
B. Viviani ◽  
J. L. Torrea
Keyword(s):  
Riesz Transforms ◽  
Laguerre Expansions

scholarly journals A symmetrized conjugacy scheme for orthogonal expansions

2013 ◽  
Vol 143 (2) ◽  
pp. 427-443 ◽  
Author(s):  
Adam Nowak ◽  
Krzysztof Stempak
Keyword(s):  
Differential Operator ◽  
Higher Order ◽  
Riesz Transforms ◽  
Orthogonal System ◽  
Order Differential Operator ◽  
Orthogonal Expansions ◽  
Partial Derivatives ◽  
Poisson Integrals ◽  
Conjugate Poisson Integrals ◽  
Classical Shape

We establish a symmetrization procedure in the context of general orthogonal expansions associated with a second-order differential operator L, a Laplacian. Combining with a unified conjugacy scheme from an earlier paper by Nowak and Stempak permits, using a suitable embedding, a differential-difference Laplacian $\mathbb{L}$ to be associated with the initially given orthogonal system of eigenfunctions of L, so that the resulting extended conjugacy scheme has the natural classical shape. This means, in particular, that the related partial derivatives decomposing $\mathbb{L}$ are skew-symmetric in an appropriate L2 space and they commute with Riesz transforms and conjugate Poisson integrals. The results also shed new light on the issue of defining higher-order Riesz transforms for general orthogonal expansions.

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.

Sign in / Sign up

Export Citation Format

Share Document