Sharp estimates of the norms of fractional derivatives of functions of several variables satisfying H?lder conditions

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• 作者：V. F. Babenko and S. A. Pichugov
• 关键词：Marchaud fractional derivative ; essentially bounded function ; Kolmogorov ; type inequality ; H?lder condition ; H?lder space
• 刊名：Mathematical Notes
• 出版年：2010
• 出版时间：February, 2010
• 年：2010
• 卷：87
• 期：1-2
• 页码：23-30
• 全文大小：589.1 KB

文摘

We prove a new sharp Kolmogorov-type inequality that estimates the uniform norm of a mixed derivative of fractional order (in the sense of Marchaud) of a function of several variables via the uniform norm of the function and its norm on H?lder spaces.