Convolution of Two Weighted Orlicz Spaces on Hypergroups

Mohammad Tabatabaie, Seyyed; Bagheri Salec, AliReza; Mohammad Tabatabaie, Seyyed; Bagheri Salec, AliReza

doi:10.15446/recolma.v54n2.93841

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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.54 no.2 Bogotá jul./dez. 2020 Epub 05-Mar-2021

https://doi.org/10.15446/recolma.v54n2.93841

Artículos originales

Convolution of Two Weighted Orlicz Spaces on Hypergroups

Convolución de dos espacios de Orlicz con pesos sobre hipergrupos

Seyyed Mohammad Tabatabaie¹^*

AliReza Bagheri Salec¹

^¹University of Qom, Qom, Iran

Abstract:

Let K be a locally compact hypergroup. In this paper, among other results we give a suficient condition for the inclusion L ^Φ1 _w (K) * L ^Φ2 _w (K) ⊆ L^Φ1 _w (K) to hold. Also, as an application, we provide a new suficient condition for the weighted Orlicz space L ^Φ _w (K) to be a convolution Banach algebra.

Keywords: Locally compact group; locally compact hypergroup; weighted Orlicz space; Young function; convolution; Banach algebra

Resumen:

Sea K un hipergrupo localmente compacto. En este artículo, entre otros resultados, damos una condición suficiente para que se cumpla la inclusión L ^Φ1 _w (K) * L ^Φ2 _w (K) ⊆ L^Φ1 _w (K). Como una aplicación de este resultado, logramos dar una nueva condición suficiente para que el espacio de Orlicz con pesos L ^Φ _w (K) sea un álgebra de Banach bajo la convolución.

Palabras clave: Grupos localmente compactos; hipergrupos localmente compactos; espacios de Orlicz con pesos; función de Young; convolución; álgebras de Banach

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Received: December 06, 2019; Accepted: May 27, 2020

^*Correspondencia: Seyyed Mohammad Tabatabaie, Department of Mathematics, University of Qom, Qom, Iran. Correo electrónico: sm.tabatabaie@qom.ac.ir. DOI: https://doi.org/10.15446/recolma.v54n2.93841

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