We consider complex-valued functions f ∈ L^1 （R^2＋）, where R＋ ：= [0,∞）, and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to o...We consider complex-valued functions f ∈ L^1 （R^2＋）, where R＋ ：= [0,∞）, and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to one of the two-dimensional Lipschitz classes Lip（a,β） for some 0 〈 α,β ≤ 1; or to one of the Zygmund classes Zyg（α,β） for some 0 〈 α,β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L^1 （R^2＋）.展开更多
基金Supported partially by the Program TMOP-4.2.2/08/1/2008-0008 of the Hungarian National Development Agency
文摘We consider complex-valued functions f ∈ L^1 （R^2＋）, where R＋ ：= [0,∞）, and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to one of the two-dimensional Lipschitz classes Lip（a,β） for some 0 〈 α,β ≤ 1; or to one of the Zygmund classes Zyg（α,β） for some 0 〈 α,β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L^1 （R^2＋）.
基金Supported by the National Nature Science Foundation of China(71271042,11401127)the Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning((2011)47)+3 种基金the Support Program of the Guangxi China Science Foundation(2014GXNSFBA118006,2013GXNSFDA019001)the Guangxi Provincial Scientic Research Projects(201204LX157,2013YB104,YB2014150)the Construct Program of the Key Discipline in Hunan Province([2011]76)the Science Foundation of Hengyang Normal University(14B30)
