Mellin transform of log-Lipschitz functions and equivalence of K-functionals and modulus of smoothness generated by the Mellin Steklov operator

被引：3

作者：

Bouhlal, A. ^{[1
]}

机构：

[1] Univ Chouaib Doukkali, Fac Sci Jurid Econom & Sociales, Lab Rech Gest Econ & Sci Sociales, El Jadida, Morocco

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2023年 / 72卷 / 02期

关键词：

Mellin transforms; Complex-valued function; Mellin derivative; Fourier analysis; FOURIER-TRANSFORMS; GROWTH;

D O I：

10.1007/s12215-022-00729-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we examine the order of magnitude of the Mellin transform for complex-valued functions belonging to the log-Lipschitz class. In addition, in the intersection of the spaces X-c(1) and X-c(2), using the Mellin Steklov operator, we construct the Mellin modulus of smoothness, and also using the Mellin derivative we define the Mellin K-functional. The second main result of our article is the proof of the equivalence between Mellin K-functionals and Mellin modulus of smoothness.

引用

页码：1239 / 1249

页数：11

共 22 条

[21] Equivalence ofK-functionals and modulus of smoothness generated by a generalized Jacobi-Dunkl transform on the real line
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Tyr, Othman
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2021, 70 (02) : 687 - 698
[22] Equivalence of K-functionals and moduli of smoothness generated by the Beltrami-Laplace operator on the spaces S(p,q)(σm-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{(p,q)}(\sigma ^{m-1})$$\end{document}
Salah El Ouadih
Radouan Daher
Othman Tyr
Faouaz Saadi
Rendiconti del Circolo Matematico di Palermo Series 2, 2022, 71 (1): : 445 - 458

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