Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical o...Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.展开更多
In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） ...In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） summable （α＋β 〈 1/p,α,β 〉 0） in the sense of Pringsheim. If α ＋ β ≥ 1/p, then there exists a continuous function f0 of bounded partial p-variation on [-π,π]^2 such that the Cesàro （C;-α,-β） means σn,m^-α,-β（f0;0,0） of the double trigonometric Fourier series of f0 diverge over cubes.展开更多
文摘Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.
文摘In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） summable （α＋β 〈 1/p,α,β 〉 0） in the sense of Pringsheim. If α ＋ β ≥ 1/p, then there exists a continuous function f0 of bounded partial p-variation on [-π,π]^2 such that the Cesàro （C;-α,-β） means σn,m^-α,-β（f0;0,0） of the double trigonometric Fourier series of f0 diverge over cubes.
