Open AccessHigher-Order Riesz Transforms in the Inverse Gaussian Setting and UMD Banach Spaces
Author(s) -
Jorge J. Betancor,
Lourdes Rodrı́guez-Mesa
Publication year - 2021
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.579
H-Index - 28
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2021/6899603
Subject(s) - inverse , mathematics , riesz transform , order (exchange) , banach space , pure mathematics , combinatorics , geometry , finance , economics
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.