摘要
主要研究了带参数的抛物型Marcinkiewicz函数μσΩ,h(f)的L2(Rn)有界性,用核的分解技术和Fourier变换估计的方法分别在当1<γ<∞,h∈Hγ(R+),Ω∈L(log L)1/γ(SnΩ1)条件下和当1<γ≤∞,h∈Ωγ(R+),Ω∈Llog+L(SnΩ1)条件下,建立了μσΩ,h(f)的L2(Rn)有界性,并推广了以前学者的结论.
This note is concerned with L^2(R^n) boundedness of parametric parabolic Marcinkiewicz function μσΩ,h(f). Under the conditions 1〈-γ〈∞,h∈Hγ'(IR)+),Ω∈L(logL)1/γ(Sn-1)) and 1〈γ≤∞,h∈△γ((IR)+),Ω∈Llog+L(Sn-1), using kernel decomposition technique and Fourier transform estimate, the L^(Rn) boundedness is obtained for μσΩ,h(f) respectively. The well-known results by before scholars are extended.
出处
《纯粹数学与应用数学》
CSCD
2010年第5期735-744,共10页
Pure and Applied Mathematics
基金
国家自然科学基金(10571014
10671158)