Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L ([0, 1)d), d≥1 into space weak - LI([0,1)^d) are studied. The maximal Orlicz space such that the Norlund logarithmic means...Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L ([0, 1)d), d≥1 into space weak - LI([0,1)^d) are studied. The maximal Orlicz space such that the Norlund logarithmic means of multiple Walsh-Fourier series for the functions from this space converge in d-dimensional measure is found.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
The (NSrlund) logarithmic means of the Fourier series of the integrable function f is:1/lnn-1∑k=1Sk(f)/n-k, where ln:=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this loga...The (NSrlund) logarithmic means of the Fourier series of the integrable function f is:1/lnn-1∑k=1Sk(f)/n-k, where ln:=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.展开更多
基金The first author is supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. M 36511/2001, T 048780by the Szechenyi fellowship of the Hungarian Ministry of Education Szo 184/200
文摘Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L ([0, 1)d), d≥1 into space weak - LI([0,1)^d) are studied. The maximal Orlicz space such that the Norlund logarithmic means of multiple Walsh-Fourier series for the functions from this space converge in d-dimensional measure is found.
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.
基金supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. M 36511/2001, T 048780by the Szechenyi fellowship of the Hungarian Ministry of Education Sz 184/2003
文摘The (NSrlund) logarithmic means of the Fourier series of the integrable function f is:1/lnn-1∑k=1Sk(f)/n-k, where ln:=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.