共查询到20条相似文献,搜索用时 15 毫秒
1.
Óscar Ciaurri 《Journal of Computational and Applied Mathematics》2009,233(3):663-666
For most orthogonal systems and their corresponding Fourier series, the study of the almost everywhere convergence for functions in Lp requires very complicated research, harder than in the case of the mean convergence. For instance, for trigonometric series, the almost everywhere convergence for functions in L2 is the celebrated Carleson theorem, proved in 1966 (and extended to Lp by Hunt in 1967).In this paper, we take the system
2.
V.V. Galatenko T.P. Lukashenko V.A. Sadovnichii 《Moscow University Mathematics Bulletin》2016,71(5):191-195
An almost everywhere convergence condition with the Weyl multiplier W111111111(n) = v n is obtained for orthorecursive expansions that converge to the expanded function in L2. 相似文献
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5.
Б. С. кашин 《Analysis Mathematica》1976,2(4):249-266
?n = 1¥ cn jn (x)\sum\limits_{n = 1}^\infty {c_n \varphi _n } (x) 相似文献
6.
M. G. Grigoryan 《Mathematical Notes》1992,51(5):447-453
Translated from Matematicheskie Zametki, Vol. 51, No. 5, pp. 35–43, May, 1992. 相似文献
7.
М. Г. Григорян 《Analysis Mathematica》1985,11(3):201-216
, . . Q
k
[0,2],k=1,2, — . F(x, y)L(T), T=[0, 2]2, G(x, y)L(T) , G(x,y)=F(x,y) Q=Q
1
×Q
2
- . 相似文献
8.
M. A. Skopina 《Journal of Mathematical Sciences》1994,71(1):2263-2268
Let f be a function summable on the two-dimensional torus with Fourier series
. The Marcinkiewicz means
. where is a function defined on [0, 1], are considered. The following theorem is proved. Let > 0 and assume that the function , concave on [0, 1], is such that (0)=1, (1)=0 and its modulus of continuity satisfies the relation (,h)=0 (log–2–(1+1/k)). Then for almost all x.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 148–156, 1991. 相似文献
9.
B. S. Kashin 《Mathematical Notes》1973,14(5):930-935
We will investigate the properties of series of functions which are unconditionally convergent almost everywhere on [0, 1]. We will establish the following theorem: If the series
k=1
f
k(x) converges unconditionally almost everywhere, then there exists a sequence {k}
1
,k , such that if
k
k
, k=1, 2,..., the series
k=1
k/k(x) converges unconditionally almost every-where.Translated from Mate matte heskie Zametki, Vol. 14, No. 5, pp. 645–654, November, 1973.The author wishes to thank Professor P. L. Ul'yanov for his help. 相似文献
10.
The purpose of this paper is to establish a class of strong limit theorems for arbitrary stochastic sequences. As corollaries, we generalize some known results. 相似文献
11.
S. V. Bochkarev 《Mathematical Notes》1968,4(2):618-623
A continuous function is constructed whose Haar-Fourier series, after a definite rearrangement of its terms, diverges almost everywhere. A function is also constructed which has the maximum degree of smoothness in the sense that if its smoothness is increased its Haar-Fourier series becomes unconditionally convergent almost everywhere.Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 211–220, August, 1968. 相似文献
12.
Joseph Rosenblatt 《Mathematische Annalen》1988,280(4):565-577
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R. M. Megrabian 《Analysis Mathematica》1988,14(1):37-47
В статье рассматрива ются множестваM N , 1≦N<∞ всех систем функций Φ={?(x)} j =1/N , заданных на [0,1] с где (ε i, j ) i, j =1/N — матрица с э лементами ± 1. Изучаетс я поведение наМ N функц ии $$\alpha _N (\Phi ) = \mathop {\sup }\limits_\sigma \mathop {\sup }\limits_{\sum a_j^2 = 1} (\int\limits_0^1 {\mathop {\sup }\limits_{1 \leqq k \leqq N} (\sum\limits_{j = 1}^k {a_j \varphi _{\sigma (j)} (x)} } )^2 dx)^{1/2} $$ гдеσ: {1, ...,N}?{1, ...,N}. Дока зьгаается, что сущест вуют абсолютные постоянн ыеc 3,c 4>0,y 0>1, такие, что для любог оN=1,2, ... иy>y 0 $$\mu _N (\{ \Phi \in {\rm M}_{\rm N} :\alpha _N (\Phi )/\left\| \Phi \right\| > y\} ) \leqq c_3 \exp [ - \exp (c_4 y)N]$$ гдеμ N — мера наM N с µ N ({Ф}) = 2?N2 дл я любой системыΦ∈M 相似文献
15.
Vitalii A. Andrienko 《Journal of Mathematical Sciences》2012,183(6):749-761
Sufficient conditions of the classical type ensuring the almost everywhere (a.e.) convergence of the nonnegative-order Riesz means of double orthogonal series are indicated. Analogies of the onedimensional results of Kolmogoroff [7] and Kaczmarz?CZygmund [5, 12] have been obtained for the Cesaro means and those of Zygmund [13] for the Riesz means. These analogies establish the a.e. equiconvergence of the lacunary subsequences of rectangular partial sums and of the entire sequence of Riesz means, generalize the corresponding results of Moricz [9] for the Cesaro a.e. summability by (C, 1, 1), (C, 1, 0), and (C, 0, 1) methods of double orthogonal series, and were announced earlier without proofs in the author??s work [3]. 相似文献
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17.
E. A. Vlasova 《Siberian Mathematical Journal》1992,33(5):784-789
Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 47–52, September–October, 1992. 相似文献
18.
On the almost everywhere convergence of ergodic averages for power-bounded operators on LP-subspaces
Earl Berkson Jean Bourgain T. A. Gillespie 《Integral Equations and Operator Theory》1991,14(5):678-715
Let X be a closed subspace of LP(), where is an arbitrary measure and 1
A(n) and (n) denote the discrete ergodic averages and Hilbert transform truncates defined by U. We extend to this setting the -a. e. convergence criteria forA(n) and (n) which V. F. Gaposhkin and R. Jajte introduced for unitary operators on L2(). Our methods lift the setting from X to p, where classical harmonic analysis and interpolation can be applied to suitable square functions. 相似文献
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20.
F. Weisz 《Acta Mathematica Hungarica》2007,116(1-2):47-59
The duality between martingale Hardy and BMO spaces is generalized for Banach space valued martingales. It is proved that if X is a UMD Banach space and f ∈ L
p(X) for some 1 < p < ∞ then the Vilenkin-Fourier series of f converges to f almost everywhere in X norm, which is the extension of Carleson’s result.
This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship
No. M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No. T043769, T047128, T047132. 相似文献