摘要
Let f be an integrable function on the unit sphere Σ n?1 of R n (n?3) and let σ N δ be the Cesàro means of order σ of the Fourier-Laplace series of f. The special value λ:=n?2/2 of σ is known as the critical index. This paper proves that and where ω(f,t)p is the 1st-order modulus of continuity of f in Lp-metric which is defined in a way different than in the classical case of n=2.
Let f be an integrable function on the unit sphere Σ n?1 of R n (n?3) and let σ N δ be the Cesàro means of order σ of the Fourier-Laplace series of f. The special value λ:=n?2/2 of σ is known as the critical index. This paper proves that and where ω(f,t)p is the 1st-order modulus of continuity of f in Lp-metric which is defined in a way different than in the classical case of n=2.
基金
Project supported by the NSF of China under the grant # 19771009
