【摘要】 设Rn是n-维欧氏空间n≥3.用Ωn表示Rn上的单位球面,对于函数f∈L（Ωn）,ENδ（f）表示其Fourier-Laplace级数的δ阶Cesaro平均所决定的等收敛算子,其中,λ:=（n-2）/2,δ是熟知的临界指标.对于0<δ≤λ,令p0:=2λ/（λ+δ）,本文主要证明了如下结果:||ENδ(f)||p0≤C（n,l)(∫Ωn|f(x)|p0(log+log+|f(x)|l(p0-1)dx+1),l>1.更多还原

【Abstract】 Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace series of f. The special value λ:= (n-2)/2 of δ is known as the critical index. For 0 < δ≤λ, we set p0 := 2λ/(λ+δ). The main aim of this paper is to prove thatwith l > 1.更多还原