Embedding theorem on spaces of homogeneous type
type: Item
instance of: scholarly article
title: Embedding theorem on spaces of homogeneous type
zbMATH Open document ID: 1032.42024
author: Yongsheng Han
author: Chin-Cheng Lin
published in: The Journal of Fourier Analysis and Applications
publication date: 2003-06-23T00:00:00Z
review text: This paper deals with embedding theorems for Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. The main result shows that if \(-\varepsilon<s_1<s_2<\varepsilon\), then 1) \(\dot B_{p_2}^{s_2,q}\subset \dot B_{p_1}^{s_1,q}\) continuously for \(0<q\leq\infty\), \(\max\{{1\over 1+\varepsilon}, {1\over 1+\varepsilon+s_1}\}<p_1\leq\infty\), \(\max\{{1\over 1+\varepsilon}, {1\over 1+\varepsilon+s_2}\}<p_2\leq\infty\), \(y-\varepsilon<s_2-1/p_2=s_1-1/p_1<\varepsilon\). 2) \(\dot F_{p_2}^{s_2,q_2}\subset \dot F_{p_1}^{s_1,q_1}\) continuously for \(\max\{{1\over 1+\varepsilon}, {1\over 1+\varepsilon+s_1}\}<p_1, q_1<\infty\), \(\max\{{1\over 1+\varepsilon}, {1\over 1+\varepsilon+s_2}\} <p_2, q_2<\infty\), \(y-\varepsilon<s_2-1/p_2=s_1-1/p_1<\varepsilon\). To prove this result they need a discrete Calderón type reproducing formula on spaces of homogeneous type.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1890483
zbMATH Keywords: Besov spaces
zbMATH Keywords: Triebel-Lizorkin spaces
zbMATH Keywords: embeddings
zbMATH Keywords: discrete Calderón formula
zbMATH Keywords: spaces of homogeneous type
reviewed by: María J. Carro
MaRDI profile type: Publication
full work available at URL: s00041-002-0014-5
OpenAlex ID: W2056629247
DOI: 10.1007/S00041-002-0014-5
description: scientific article; zbMATH DE number 1890483