Stummel class of Morrey spaces
type: Item
instance of: scholarly article
title: Stummel class of Morrey spaces
zbMATH Open document ID: 1113.46022
author: N. E. Zubov
published in: Southeast Asian Bulletin of Mathematics
publication date: 2006-12-06T00:00:00Z
review text: Let \[ \mathcal{M}_{1,\varphi}=\left\{f\in L^1_{\text{loc}}(\mathbb{R}^n)\,\biggl|\, \sup_B \frac{1}{\varphi(B)}\int_B|f(y)|\,dy <\infty\right\} \] be the generalized Morrey space, where \(\psi: (0,\infty ) \to (0,\infty)\) satisfies the doubling condition. The authors study relations between the space \(\mathcal{M}_{1,\varphi}\) and the class \[ S_\psi = \left\{f\in L^p_{\text{loc}}(\mathbb{R}^n)\,\Bigl|\, \lim_{r\to 0} \psi_f(r)\right\}, \quad \psi_f(r) = \sup_{x\in\mathbb{R}^n}\int_{|x-y|<r} |f(y)| \frac{\psi(|x-y|)}{|x-y|^n}\,dy . \]
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 5077520
zbMATH Keywords: Morrey spaces
zbMATH Keywords: Stummel class
reviewed by: S. G. Samko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5077520