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
Poets often express their ideas and attitudes through their poems,like American poet Robert Frost,British poet A.E Housman and Chinese Cao xueqin.The paper compares pessimism towards life of the three poets by analyzi...Poets often express their ideas and attitudes through their poems,like American poet Robert Frost,British poet A.E Housman and Chinese Cao xueqin.The paper compares pessimism towards life of the three poets by analyzing their poems.展开更多
In this paper, a strong limit theorem on gambling strategy for binary Bernoulli sequence, (i.e.) irregularity theorem, is extended to random selection for dependent m-valued random variables, via using a new method-di...In this paper, a strong limit theorem on gambling strategy for binary Bernoulli sequence, (i.e.) irregularity theorem, is extended to random selection for dependent m-valued random variables, via using a new method-differentiability on net. Furthermore, by allowing the selection function to take value in finite interval [-M,M], the conception of random selection is generalized.展开更多
A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as ...A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as follows：Theorem Suppose f ∈ L（En-1）, n≥ 3. If f satisfies the condition1/θ^n-1∫D（x,θ）｜f（y）-f（x）｜dy=O（1/｜logθ｜）,as θ→0＋,at every point x in a set E of positive measure in Σn-1, then the Cesàro means of critical order ,n-2/2 of the Fourier-Laplace series of f converge to f at almost every point x in E.展开更多
We prove the boundedness from Lp（T2） to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf（x, y） presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of in...We prove the boundedness from Lp（T2） to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf（x, y） presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by ｜y′｜ 〉 ｜x′｜, and presenting phases λ（Ax ＋ By） with 0≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A1 B and A involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.展开更多
Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, pro...Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, provided that the exceptional set E has σ-finite H^1-measure.Moreover, f has finite distortion, differentiable a.e. and the Jacobian Jf 〉 0 a.e.展开更多
A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of the Fejér （or （C, 1）） means of functions on unbounded Vilenkin groups. There are several papers of the author of this pa...A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of the Fejér （or （C, 1）） means of functions on unbounded Vilenkin groups. There are several papers of the author of this paper concerning this. That is, we know the a.e. convergence σnf → f （n → ∞） for functions f ∈ L^p, where p 〉 1 （Journal of Approximation Theory, 101（1）, 1-36, （1999）） and also the a.e. convergence σMnf → f （n → ∞） for functions f ∈ L^1 （Journal of Approximation Theory, 124（1）, 25-43, （2003））. The aim of this paper is to prove the a.e. relation limn→∞ σnf = f for each integrable function f on any rarely unbounded Vilenkin group. The concept of the rarely unbounded Vilenkin group is discussed in the paper. Basically, it means that the generating sequence m may be an unbounded one, but its ＂big elements＂ are not ＂too dense＂.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.
文摘Poets often express their ideas and attitudes through their poems,like American poet Robert Frost,British poet A.E Housman and Chinese Cao xueqin.The paper compares pessimism towards life of the three poets by analyzing their poems.
文摘In this paper, a strong limit theorem on gambling strategy for binary Bernoulli sequence, (i.e.) irregularity theorem, is extended to random selection for dependent m-valued random variables, via using a new method-differentiability on net. Furthermore, by allowing the selection function to take value in finite interval [-M,M], the conception of random selection is generalized.
基金supported by the NSF of China,No.10471010the Natural Science Foundation of Tianjin Normal University,52LJ32The Planned Project of the Development Foundation of Science and Technology of Universities in Tianjin
文摘A covering lemma on the unit sphere is established and then is applied to establish an almost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unit sphere which can be stated as follows：Theorem Suppose f ∈ L（En-1）, n≥ 3. If f satisfies the condition1/θ^n-1∫D（x,θ）｜f（y）-f（x）｜dy=O（1/｜logθ｜）,as θ→0＋,at every point x in a set E of positive measure in Σn-1, then the Cesàro means of critical order ,n-2/2 of the Fourier-Laplace series of f converge to f at almost every point x in E.
文摘We prove the boundedness from Lp（T2） to itself, 1 〈 p 〈∞, of highly oscillatory singular integrals Sf（x, y） presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by ｜y′｜ 〉 ｜x′｜, and presenting phases λ（Ax ＋ By） with 0≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A1 B and A involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.
基金Supported partially by the Academy of Finland(Grant No.131477)the Magnus Ehrnrooth foundation
文摘Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, provided that the exceptional set E has σ-finite H^1-measure.Moreover, f has finite distortion, differentiable a.e. and the Jacobian Jf 〉 0 a.e.
基金the Hungarian National Foundation for Scientific Research(OTKA),Grant No.M36511/2001 and T 048780
文摘A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of the Fejér （or （C, 1）） means of functions on unbounded Vilenkin groups. There are several papers of the author of this paper concerning this. That is, we know the a.e. convergence σnf → f （n → ∞） for functions f ∈ L^p, where p 〉 1 （Journal of Approximation Theory, 101（1）, 1-36, （1999）） and also the a.e. convergence σMnf → f （n → ∞） for functions f ∈ L^1 （Journal of Approximation Theory, 124（1）, 25-43, （2003））. The aim of this paper is to prove the a.e. relation limn→∞ σnf = f for each integrable function f on any rarely unbounded Vilenkin group. The concept of the rarely unbounded Vilenkin group is discussed in the paper. Basically, it means that the generating sequence m may be an unbounded one, but its ＂big elements＂ are not ＂too dense＂.
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.
