The Experts below are selected from a list of 2691 Experts worldwide ranked by ideXlab platform
Karoly Nagy - One of the best experts on this subject based on the ideXlab platform.
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strong approximation by Marcinkiewicz means of two dimensional walsh kaczmarz fourier series
Analysis Mathematica, 2016Co-Authors: Ushangi Goginava, Karoly NagyAbstract:In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.
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weak type inequality for the maximal operator of walsh kaczmarz Marcinkiewicz means
Acta Mathematica Scientia, 2016Co-Authors: Ushangi Goginava, Karoly NagyAbstract:Abstract The main aim of this article is to prove that the maximal operator σ * κ 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.
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strong approximation by Marcinkiewicz means of two dimensional walsh kaczmarz fourier series
Constructive Approximation, 2012Co-Authors: Ushangi Goginava, Karoly NagyAbstract:In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-Fourier series of the continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is best possible.
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on the l1 norm of the weighted maximal function of walsh Marcinkiewicz kernels
2012Co-Authors: Karoly NagyAbstract:The L1 norm of the maximal function of Walsh-Marcinkiewicz kernel is infinite. Thus, we have to use some weight function to “pull it back” to the finite.
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on the Marcinkiewicz fejer means of double fourier series with respect to the walsh kaczmarz system
Studia Scientiarum Mathematicarum Hungarica, 2009Co-Authors: Gyorgy Gat, Ushangi Goginava, Karoly NagyAbstract:The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejer means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H pq into Lorentz space L pq for every p > 2/3 and 0 < q ≦ ∞. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejer means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σ n ( f, x 1 , x 2 ) → ( x 1 , x 2 ) a.e. as n → ∞.
Ushangi Goginava - One of the best experts on this subject based on the ideXlab platform.
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strong approximation by Marcinkiewicz means of two dimensional walsh kaczmarz fourier series
Analysis Mathematica, 2016Co-Authors: Ushangi Goginava, Karoly NagyAbstract:In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh–Kaczmarz–Fourier series of every continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is the best possible.
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weak type inequality for the maximal operator of walsh kaczmarz Marcinkiewicz means
Acta Mathematica Scientia, 2016Co-Authors: Ushangi Goginava, Karoly NagyAbstract:Abstract The main aim of this article is to prove that the maximal operator σ * κ 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.
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strong approximation by Marcinkiewicz means of two dimensional walsh kaczmarz fourier series
Constructive Approximation, 2012Co-Authors: Ushangi Goginava, Karoly NagyAbstract:In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-Fourier series of the continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is best possible.
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on the Marcinkiewicz fejer means of double fourier series with respect to the walsh kaczmarz system
Studia Scientiarum Mathematicarum Hungarica, 2009Co-Authors: Gyorgy Gat, Ushangi Goginava, Karoly NagyAbstract:The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejer means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H pq into Lorentz space L pq for every p > 2/3 and 0 < q ≦ ∞. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejer means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σ n ( f, x 1 , x 2 ) → ( x 1 , x 2 ) a.e. as n → ∞.
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the weak type inequality for the maximal operator of the Marcinkiewicz fejer means of the two dimensional walsh fourier series
Journal of Approximation Theory, 2008Co-Authors: Ushangi GoginavaAbstract:The main aim of this paper is to prove that the maximal operator @s^* of the Marcinkiewicz-Fejer means of the two-dimensional Walsh-Fourier series is bounded from the Hardy space H"2"/"3 to the space weak-L"2"/"3.
Emmanuel Rio - One of the best experts on this subject based on the ideXlab platform.
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a maximal inequality and dependent Marcinkiewicz zygmund strong laws
Annals of Probability, 1995Co-Authors: Emmanuel RioAbstract:This paper contains some extension of Kolmogorov's maximal inequality to dependent sequences. Next we derive dependent Marcinkiewicz-Zygmund type strong laws of large numbers from this inequality. In particular, for stationary strongly mixing sequences (X i ) i ∈ Z with sequence of mixing coefficients (α n ) n≥0 , the Marcinkiewicz-Zygmund SLLN of order p holds if ∫ 0 1 [α -1 (t)] p-1 Q p (t) dt < ∞, where α -1 denotes the inverse function of the mixing rate function t → α [t] and Q denotes the quantile function of |X 0 |. The condition is obtained by an interpolation between the condition of Doukhan, Massart and Rio implying the CLT (p = 2) and the integrability of |X 0 | implying the usual SLLN (p = 1). Moreover, we prove that this condition cannot be improved for stationary sequences and power-type rates of strong mixing.
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a maximal inequality and dependent Marcinkiewicz zygmund strong laws
Annals of Probability, 1995Co-Authors: Emmanuel RioAbstract:This paper contains some extension of Kolmogorov's maximal inequality to dependent sequences. Next we derive dependent Marcinkiewicz-Zygmund type strong laws of large numbers from this inequality. In particular, for stationary strongly mixing sequences $(X_i)_{i\in\mathbb{Z}$ with sequence of mixing coefficients $(\alpha_n)_{n\geq 0}$, the Marcinkiewicz-Zygmund SLLN of order $p$ holds if $\int^1_0\lbrack\alpha^{-1}(t)\rbrack^{p-1}Q^p(t)dt < \infty,$ where $\alpha^{-1}$ denotes the inverse function of the mixing rate function $t \rightarrow \alpha_{\lbrack t\rbrack}$ and $Q$ denotes the quantile function of $|X_0|$. The condition is obtained by an interpolation between the condition of Doukhan, Massart and Rio implying the CLT $(p = 2)$ and the integrability of $|X_0|$ implying the usual SLLN $(p = 1)$. Moreover, we prove that this condition cannot be improved for stationary sequences and power-type rates of strong mixing.
V N Temlyakov - One of the best experts on this subject based on the ideXlab platform.
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entropy numbers and Marcinkiewicz type discretization
Journal of Functional Analysis, 2021Co-Authors: Feng Dai, V N Temlyakov, A Prymak, Alexei Shadrin, Sergey TikhonovAbstract:Abstract This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied to establish a Marcinkiewicz-type discretization result for these classes.
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entropy numbers and Marcinkiewicz type discretization theorem
arXiv: Classical Analysis and ODEs, 2020Co-Authors: Feng Dai, V N Temlyakov, A Prymak, Alexei Shadrin, Sergey TikhonovAbstract:This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied to establish a Marcinkiewicz type discretization theorem for integral norms of functions from a given finite dimensional subspace.
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the Marcinkiewicz type discretization theorems
Constructive Approximation, 2018Co-Authors: V N TemlyakovAbstract:This paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications, but there is no systematic study of it. We present here a new technique, which works well for discretization of the integral norm. It is a combination of probabilistic technique, based on chaining, and results on the entropy numbers in the uniform norm.
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the Marcinkiewicz type discretization theorems
arXiv: Numerical Analysis, 2017Co-Authors: V N TemlyakovAbstract:The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which works well for discretization of the integral norm. It is a combination of probabilistic technique, based on chaining, with results on the entropy numbers in the uniform norm.
Soo Hak Sung - One of the best experts on this subject based on the ideXlab platform.
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Marcinkiewicz zygmund type strong law of large numbers for pairwise i i d random variables
Journal of Theoretical Probability, 2014Co-Authors: Soo Hak SungAbstract:Etemadi (in Z. Wahrscheinlichkeitstheor. Verw. Geb. 55, 119–122, 1981) proved that the Kolmogorov strong law of large numbers holds for pairwise independent identically distributed (pairwise i.i.d.) random variables. However, it is not known yet whether the Marcinkiewicz–Zygmund strong law of large numbers holds for pairwise i.i.d. random variables. In this paper, we obtain the Marcinkiewicz–Zygmund type strong law of large numbers for pairwise i.i.d. random variables {Xn,n≥1} under the moment condition E|X1|p(loglog|X1|)2(p−1)<∞, where 1
