简介:为在上可辨的功能(0,1)有检验了某三角法的系列(1)的工具(2)。节2包含一些基本估计。在节3,作者介绍二条主要定理,它对应于提议1,中的2个[3]。
简介:The(Nrlund)logarithmicmeansoftheFourierseriesoftheintegrablefunctionfis:1/l_nsumfromk=1ton-1S_k(f)/(n-k),wherel_n:=sumfromk=1ton-11/kInthispaperwediscusssomeconvergenceanddivergencepropertiesofthislogarithmicmeansoftheWalsh-Fourierseriesoffunctionsintheuniform,andintheL~1Lebesguenorm.Amongothers,asanapplicationofourdivergenceresultswegiveanegativeanswertoaquestionofMóriczconcerningtheconvergenceoflogarithmicmeansinnorm.
简介:Inthispaper,weconsiderthealmosteverywhereconvergencofBochner-RieszmeansbelowthecriticalindexinBesselpotentialspacesanda>0)andfindouttherelationbetweentheindexofBochner-Rieszmeansandthedegreeofsmoothnessoffunctions.
简介:InthispaperwestudytheapproximationonsetoffullmeasureforfunctionsinSobolevspacesL_m~1(R~n)(m∈N)byBochner-RieszmeansofconjugaleFourierintegralsbelowthecriticalindex.AtheoremconcerningthepreciseapproximationorderswithrelationtothenumbermofspaceL_m~1(R~n)andtheindexofBochner-Rieszmeansisobtained.