Some inclusion theorems for Orlicz and Musielak-Orlicz type spaces
type: Item
instance of: scholarly article
title: Some inclusion theorems for Orlicz and Musielak-Orlicz type spaces
zbMATH Open document ID: 0877.47017
DOI: 10.1007/BF01759260
author: Carlo Bardaro
author: Gianluca Vinti
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1997-12-08T00:00:00Z
review text: The integral operators of type \[ (Kf)(t)= \int_a^b K(t,s)f(s)ds \] are studied where \(]a,b[\) is a bounded interval on \(\mathbb{R}^+\), \(K\) is a (not necessarily homogeneous) kernel, and \(f\) is a function from Orlicz or Musielak-Orlicz type space \(L^\varphi(]a,b[)\). Some estimates are obtained that imply the property \[ f\in L^\varphi(]a,b[) \Rightarrow Kf\in L^\varphi (]a,b]). \] An interesting (strict in general) inclusion \[ L^\varphi(]a,b[)\subset \bigcap_{\alpha\in ]0,1[} L^{\varphi,\alpha} (]a,b[) \] is given where \(L^{\varphi,\alpha}\) denotes the fractional Orlicz space of order \(\alpha\in [0,1]\) which is defined using a fractional derivative.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 878448
zbMATH Keywords: integral operators
zbMATH Keywords: Musielak-Orlicz type space
zbMATH Keywords: fractional Orlicz space
reviewed by: Alexander A. Mekler
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759260
OpenAlex ID: W2082642148
description: scientific article; zbMATH DE number 878448