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1.
Péter Kórus 《Czechoslovak Mathematical Journal》2018,68(4):987-996
We extend the results of paper of F.Móricz (2010), where necessary conditions were given for the L1-convergence of double Fourier series. We also give necessary and sufficient conditions for the L1-convergence under appropriate assumptions. 相似文献
2.
Bao-rong Wei 《高校应用数学学报(英文版)》2009,24(4):402-410
Very recently, Yu, Le and Zhou introduced the so called △B1^* and △B2^* conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series. In fact, the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series, where coefficients may have different signs. 相似文献
3.
P. Kórus 《Acta Mathematica Hungarica》2010,126(4):369-380
Chaundry and Jolliffe [1] proved that if a
k
is a nonnegative sequence tending monotonically to zero, then a necessary and sufficient condition for the uniform convergence
of the series Σ
k=1∞
a
k
sin kx is lim
k→∞
ka
k
= 0. Lately, S. P. Zhou, P. Zhou and D. S. Yu [4] generalized this classical result. In this paper we propose new classes
of sequences for which we get the extended version of their results. Moreover, we generalize the results of S. Tikhonov [2]
on the L
1-convergence of Fourier series. 相似文献
4.
It is proved that the complex double Fourier series of an integrable functionf(x, y) with coefficients cjk satisfying certain conditions, will converge in L1-norm. The conditions used here are the combinations of Tauberian condition of Hardy-Karamata kind and its limiting case.
This paper extends the result of Bray [1] to complex double Fourier series.
An erratum to this article is available at . 相似文献
5.
We study hereL 1-convergence of a complex trigonometric sum and obtain a new necessary and sufficient condition for theL 1-convergence of Fourier series. 相似文献
6.
Jia Gao 《高校应用数学学报(英文版)》2007,22(2):174-180
Let L^p(Ω, H^n) indicate the L^P-space of the maps for Heisenberg group target. In this paper some new properties are obtained for the space L^p(Ω, H^n) 相似文献
7.
S. A. Stasyuk 《Ukrainian Mathematical Journal》2004,56(11):1849-1863
We obtain estimates exact in order for the best approximations and Kolmogorov and trigonometric widths of the classes B
p,θ
Ω
of periodic functions of many variables in the space L
q
for certain values of the parameters p and q.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1557–1568, November, 2004. 相似文献
8.
Jesse Peterson 《Inventiones Mathematicae》2009,175(2):417-433
We introduce the notion of L
2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing
of 1-cohomology into the left regular representation of a group. We show that L
2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that if M is a free product
of diffuse von Neumann algebras, or if M=LΓ where Γ is a finitely generated group with β1
(2)(Γ)>0, then any nonamenable regular subfactor of M is prime and does not have properties Γ or (T). In particular this gives a new approach for showing solidity for a free group
factor thus recovering a well known recent result of N. Ozawa. 相似文献
9.
Brian Clarke 《Annals of Global Analysis and Geometry》2011,39(2):131-163
We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate
the topology on the manifold of metrics induced by the distance function of the L
2 Riemannian metric—so-called because it induces an L
2 topology on each tangent space. It turns out that this topology on the tangent spaces gives rise to an L
1-type topology on the manifold of metrics itself. We study this new topology and its completion, which agrees homeomorphically
with the completion of the L
2 metric. We also give a user-friendly criterion for convergence (with respect to the L
2 metric) in the manifold of metrics. 相似文献
10.
Heinrich P. Lotz 《Positivity》2008,12(1):119-132
We show that in the dual of Weak L1 the subspace of all rearrangement invariant continuous linear functionals is lattice isometric to a space L1(μ) and is the linear hull of the maximal elements of the dual unit ball. We also show that the dual of Weak L1 contains a norm closed weak* dense ideal which is lattice isometric to an ℓ1-sum of spaces of type C(K).
Helmut H. Schaefer in memoriam 相似文献
11.
Patrick LaVictoire 《Journal d'Analyse Mathématique》2011,113(1):241-263
We present a modified version of Buczolich and Mauldin’s proof that the sequence of square numbers is universally L
1-bad. We extend this result to a large class of sequences, including the dth powers and the set of primes. Furthermore, we show that any subsequence of the averages taken along these sequences is
also universally L
1-bad. 相似文献
12.
For any complex valued L
p
-function b(x), 2 ≤ p < ∞, or L
∞-function with the norm ‖b↾L
∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d
2/dx
2 + x
2 + b(x) in L
2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L
2(ℝ). 相似文献
13.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
14.
We give a characterization of structurally stable diffeomorphisms by making use of the notion of L
p
-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C
1-interior of the set of diffeomorphisms having L
p
-shadowing property. 相似文献
15.
Marius A. S. Irgens 《Mathematische Zeitschrift》2004,247(3):611-617
Let be a bounded domain in Cn and let L2h() be the L2-holomorphic functions on . We show that the envelope of holomorphy and the L2h()-envelope of holomorphy of differ by at most a pluripolar set.Mathematics Subject Classification (2000): 32D10, 32A36, 32U30This article is based on work the author did during his Ph.D. studies at the University of Michigan under the supervision of John Erik Fornæss. 相似文献
16.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
17.
We show that for each positive integerk there is ak×k matrixB with ±1 entries such that puttingE to be the span of the rows of thek×2k matrix [√kI
k,B], thenE,E
⊥ is a Kashin splitting: TheL
1
2k
and theL
2
2k
are universally equivalent on bothE andE
⊥. Moreover, the probability that a random ±1 matrix satisfies the above is exponentially close to 1.
Supported by the Israel Science Foundation. 相似文献
18.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
19.
Functions whose translates span L
p
(R) are called L
p-cyclic functions. For a fixed
p \memb [1, \infty], we construct Schwartz-class functions which are L
r
-cyclic for r > p and not L
r
-
cyclic for r \le p. We then construct Schwartz-class functions which are L
r
-cyclic for r \ge p and
not L
r
-cyclic for r < p. The constructions differ for p \memb (1, 2) and p > 2. 相似文献
20.
<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups
We determine the L
2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the
L
2-cohomology of left-orderable groups, and deduce the non-L
2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.
Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613. 相似文献