摘要
The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p<∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
The present paper deals with best onesided approximation rate in L p spaces n(f) L p of f∈C 2π. Although it is clear that the estimate n(f) L p≤C‖f‖ L p cannot be correct for all f∈L p 2π in case p<∞, the question whether n(f) L p≤Cω(f,n -1) L p or n(f) L p≤CE n(f) L p holds for f∈C 2π remains totally untouched. Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
基金
Supported in part by National and Zhejiang Provincial Natural Science Foundations of China.Partof the work contained in this paper was done while the second named author was visiting Simon Fraser University,Canada,he thanks Dr.P.B.Borwein and the Depa
