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
收藏
页码：1239 / 1249
页数：11
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