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

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 ON LITTLEWOOD-PALEY FUNCTIONS ASSOCIATED WITH BESSEL OPERATORS

2009 ◽  
Vol 51 (1) ◽  
pp. 55-70 ◽  
Author(s):  
J. J. BETANCOR ◽  
J. C. FARIÑA ◽  
A. SANABRIA
Keyword(s):  
Higher Order ◽  
Doubling Measure ◽  
Homogeneous Type ◽  
Type Space ◽  
Bessel Operators ◽  
Homogeneous Type Space

AbstractIn this paper, we study Lp-boundedness properties for higher order Littlewood-Paley g-functions in the Bessel setting. We use the Calderón-Zygmund theory in a homogeneous-type space (in the sense of Coifman and Weiss) ((0, ∞), d, γα), where d represents the usual metric on (0, ∞) and γα denotes the doubling measure on (0, ∞) with respect to d defined by dγα(x) = x2α+1dx, with α > −1/2.

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 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 Maximal operators, Riesz transforms and Littlewood–Paley functions associated with Bessel operators on BMO

2010 ◽  
Vol 363 (1) ◽  
pp. 310-326 ◽  
Author(s):  
J.J. Betancor ◽  
A. Chicco Ruiz ◽  
J.C. Fariña ◽  
L. Rodríguez-Mesa
Keyword(s):  
Riesz Transforms ◽  
Maximal Operators ◽  
Bessel Operators

Riesz transforms related to Bessel operators

2007 ◽  
Vol 137 (04) ◽  
pp. 701-725 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan C. C. Fariña ◽  
Dariusz Buraczewski ◽  
Teresa Martínez ◽  
José L. Torrea
Keyword(s):  
Riesz Transforms ◽  
Bessel Operators

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.

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