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Corrigendum to: Lipschitz conditions for the generalized Fourier transform associated with the Jacobi--Cherednik operator on ℝ

Corrigendum to: Lipschitz conditions for the generalized Fourier transform associated with the... Adv. Pure Appl. Math. 2017; 8 (1):77­78 Corrigendum Rabiaa Ghabi and Maher Mili* Corrigendum to: Lipschitz conditions for the generalized Fourier transform associated with the Jacobi­Cherednik operator on DOI: 10.1515/apam-2016-0102 Received October 26, 2016; accepted October 27, 2016 Corrigendum to: R. Ghabi and M. Mili, Lipschitz conditions for the generalized Fourier transform associated with the Jacobi­Cherednik operator on , Adv. Pure Appl. Math. 7 (2016), 51­62 Definition 3.1 and Theorem 3.1 of [2] should be replaced by the following: Definition 1. Let < < . A function f L p ( , A(x)dx) is said to be in the Lipschitz class, denoted by Lip(, p), if it satisfies h f + -h f - f p, A = O(h ) as h . (1) Theorem 1. Let f be in the class Lip(, p), where < < and < p , and let p be the conjugate component of p. Then Ff belongs to L ([ , +[, d ()) for all satisfying p( + ) p < (p - )( + ) + p p- To prove Theorem 1, we need the following lemma: Lemma 1. Let > - , - and x > . Then, for http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Corrigendum to: Lipschitz conditions for the generalized Fourier transform associated with the Jacobi--Cherednik operator on ℝ

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Publisher
de Gruyter
Copyright
Copyright © 2017 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam-2016-0102
Publisher site
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Abstract

Adv. Pure Appl. Math. 2017; 8 (1):77­78 Corrigendum Rabiaa Ghabi and Maher Mili* Corrigendum to: Lipschitz conditions for the generalized Fourier transform associated with the Jacobi­Cherednik operator on DOI: 10.1515/apam-2016-0102 Received October 26, 2016; accepted October 27, 2016 Corrigendum to: R. Ghabi and M. Mili, Lipschitz conditions for the generalized Fourier transform associated with the Jacobi­Cherednik operator on , Adv. Pure Appl. Math. 7 (2016), 51­62 Definition 3.1 and Theorem 3.1 of [2] should be replaced by the following: Definition 1. Let < < . A function f L p ( , A(x)dx) is said to be in the Lipschitz class, denoted by Lip(, p), if it satisfies h f + -h f - f p, A = O(h ) as h . (1) Theorem 1. Let f be in the class Lip(, p), where < < and < p , and let p be the conjugate component of p. Then Ff belongs to L ([ , +[, d ()) for all satisfying p( + ) p < (p - )( + ) + p p- To prove Theorem 1, we need the following lemma: Lemma 1. Let > - , - and x > . Then, for

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Jan 1, 2017

References