Boundedness of the Equiconvergent Operators on the Sphere
Received:June 07, 1999  
Key Words: equiconvergent operators   fourier-laplace series.  
Fund Project:Supported by NNSF of China (19771009)
Author NameAffiliation
ZHA NG Xi-rong Dept. of Fund. Sci.
North China Electric Power Univ.
Beijing
China 
DAI Feng Dept. of Math.
Beijing Normal University
China 
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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 that (?) with l > 1.
Citation:
DOI:10.3770/j.issn:1000-341X.2002.03.003
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