Inequalities for Partial Moduli of Continuity and聽Partial Derivatives

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• 作者：V. I. Kolyada (1) viktor.kolyada@kau.se
  F. J. P茅rez L谩zaro (2) javier.perezl@unirioja.es
• 关键词：Moduli of continuity &#8211 ; Gagliardo&#8211 ; Nirenberg type inequalities &#8211 ; Sobolev spaces &#8211 ; Besov norms &#8211 ; Embeddings &#8211 ; Rearrangements
• 刊名：Constructive Approximation
• 出版时间：August 2011
• 出版年：2011
• 期刊代码：34_0176-4276
• 类别：bs
• 卷：34
• 期：1
• 页码：23-59
• 数据来源：sp

摘要

We obtain pointwise and integral type estimates of higher-order partial moduli of continuity in C via partial derivatives. Also, a Gagliardo–Nirenberg type inequality for partial derivatives in a fixed direction is proved. Our methods enable us to study the case when different partial derivatives belong to different spaces, including the space L 1.