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
Let f be an H-periodic HOlder continuous function of two real variables.The error ｜｜f-Nn （p;f）｜｜ is estimated in the uniform norm and in the Holder norm,where p=（pk）k=0∞is a nonincreasing sequence of positive...Let f be an H-periodic HOlder continuous function of two real variables.The error ｜｜f-Nn （p;f）｜｜ is estimated in the uniform norm and in the Holder norm,where p=（pk）k=0∞is a nonincreasing sequence of positive numbers and Nn （p;f） is thenth Norlund mean of hexagonal Fourier series of f with respect to p = （pk）k∞=0.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
It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This i...It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.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.
基金supported by Balikesir University. Grant Number: 2014/49
文摘Let f be an H-periodic HOlder continuous function of two real variables.The error ｜｜f-Nn （p;f）｜｜ is estimated in the uniform norm and in the Holder norm,where p=（pk）k=0∞is a nonincreasing sequence of positive numbers and Nn （p;f） is thenth Norlund mean of hexagonal Fourier series of f with respect to p = （pk）k∞=0.
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.
基金the Hungarian National Foundation for Scientific Research(OTKA)(Grant No.T048780)the Georgian National Foundation for Scientific Research(Grant No.GNSF/ST07/3-171)
文摘It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.
