The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck ) be a decreasing real sequence with ck＝o( 1/(logk)r )γ ) for some γ＞ ...The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck ) be a decreasing real sequence with ck＝o( 1/(logk)r )γ ) for some γ＞ 1.Then
g(x) ＝∞∑k=1ckκk(x), f(x) ＝∞∑k=1 ck/k kk(x)
are integrable functions and f(x) is a.e. dyadic (or Butzer and Wagner) differentiable with
f[1](x) ＝ g(x)
for a.e. x∈ [0,1). The function κk means the kth Walsh-Kaczmarz function.展开更多
The main aim of this article is to prove that the maximal operator σ_κ~*of the Marcinkiewicz-Fejér means of the two-dimensional Fourier series with respect to WalshKaczmarz system is bounded from the Hardy spac...The main aim of this article is to prove that the maximal operator σ_κ~*of the Marcinkiewicz-Fejér means of the two-dimensional Fourier series with respect to WalshKaczmarz system is bounded from the Hardy space H_(2/3)to the space weak-L_(2/3).展开更多
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fejr means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0 < p ≤ 1/2.
基金Research supported by the Hungarian"M uvel odesi es Kozoktatosi Miniszterium",grant no.FKFP0182/200O,the Bolyai Fellowship of the Hungarian Academy of Science and the Hungarian National Foundation for Scientific Research(OTKA),grant no.M 36511/2001.
文摘The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck ) be a decreasing real sequence with ck＝o( 1/(logk)r )γ ) for some γ＞ 1.Then
g(x) ＝∞∑k=1ckκk(x), f(x) ＝∞∑k=1 ck/k kk(x)
are integrable functions and f(x) is a.e. dyadic (or Butzer and Wagner) differentiable with
f[1](x) ＝ g(x)
for a.e. x∈ [0,1). The function κk means the kth Walsh-Kaczmarz function.
基金supported by project TMOP-4.2.2.A-11/1/KONV-2012-0051,Shota Rustaveli National Science Foundation grant no.13/06(Geometry of function spaces,interpolation and embedding theorems)
文摘The main aim of this article is to prove that the maximal operator σ_κ~*of the Marcinkiewicz-Fejér means of the two-dimensional Fourier series with respect to WalshKaczmarz system is bounded from the Hardy space H_(2/3)to the space weak-L_(2/3).
基金supported by Shota Rustaveli National Science Foundation grant no.13/06(Geometry of function spaces,interpolation and embedding theorems)
文摘The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fejr means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0 < p ≤ 1/2.
