球面上等收敛算子的有界性(英文)

Boundedness of the Equiconvergent Operators on the Sphere

英文关键词:equiconvergent operators  fourier-laplace series.

中文摘要:

      设Rⁿ 是n-维欧氏空间n≥3.用Ω_n表示Rⁿ 上的单位球面,对于函数f∈L（Ω_n）,E_N^δ（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:

英文摘要:

      Let Rⁿ be an n-dimensional Euclidean space with n≥ 3. Denote by Ω_n the unit sphere in Rⁿ. For a function f∈L(Ω_n) we denote by E_N^δ(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 that (?) with l > 1.