A Remark on a Weighted Landau Inequality of Kwong and Zettl
نویسندگان
چکیده
In this note we extend a Theorem of Kwong and Zettl concerning the inequality Z 1 0 t ju 0 j p K Z 1 0 t juj p 1=2 Z 1 0 t ju 00 j p 1=2 to all ; ; such that = (+)=2 except for the triple: = p ?1, = ?1, = ?1?p. In this case the inequality is false; however u satisses the inequality Z 1 0 t ju 0 j p K 1 (Z 1 0 t juj p 1=2 Z 1 0 t ju 00 j p 1=2 + Z 1 0 t juj p) : 1. Notation. Let I = (a; b), ?1 a < b 1, and \AC loc (I)" denote the class of locally absolutely continuous functions on I. If , are real numbers deene
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