The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H...The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.展开更多
The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.
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 withare integrable functions and f(x) is a....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 withare integrable functions and f(x) is a. e. dyadic (or Butzer and Wagner) differentiate withThe function Kk means the kth Walsh-Kaczmarz function.展开更多
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^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H2/3 to the space weak-L2/3.
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-Fej′er 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 withare integrable functions and f(x) is a. e. dyadic (or Butzer and Wagner) differentiate withThe function Kk means the kth Walsh-Kaczmarz function.
