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61.
JPC – Journal of Planar Chromatography – Modern TLC - Among forced-flow layer chromatographic techniques, the centrifugally-driven variety was first developed, and named centrifugal... 相似文献
62.
Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2012,390(1):188-196
Motivated by the notion of Lebesgue summability of trigonometric series, we define the Lebesgue summability of trigonometric integrals in terms of the symmetric differentiability of the sum of the formally integrated trigonometric integral in question. We extend two theorems of Zygmund from trigonometric series to integrals, and one of them even in a more general form. 相似文献
63.
We prove [1, Theorems 1 and 2] under weaker conditions and in a simpler way than we did in the cited paper.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
64.
Summary We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H1 to L1, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T2 and R2. 相似文献
65.
Ferenc Móricz 《Periodica Mathematica Hungarica》2011,62(1):61-73
The well-known characterization indicated in the title involves the moving maximal dyadic averages of the sequence (X
k
: k = 1, 2, …) of random variables in Probability Theory. In the present paper, we offer another characterization of the SLLN
which does not require to form any maximum. Instead, it involves only a specially selected sequence of moving averages. The
results are also extended for random fields (X
kℓ: k, ℓ = 1, 2, …). 相似文献
66.
A theorem of Ferenc Lukács states that if a periodic function
is integrable in Lebesgue"s sense and has a discontinuity of first kind at some point
, then the
th partial sum of the conjugate series to its trigonometric Fourier series at
divided by
converges to
as
. An analogue of this theorem for Walsh–Fourier series was proved by Rafat Riad. The main aim of the present paper is to extend the latter result from single to double Wals–Fourier series. We consider also functions of two variables which are of bounded variation over a rectangle in the sense of Hardy and Krause. Among others, we present a proof of the existence of the so-called sector limits of such functions at each point. 相似文献
67.
We study the strong approximation properties of the Cesáro means of order δ of the Fourier--Laplace expansion of functions integrable on the unit sphere S n-1, where δ ≥λ? (n-2)/2, the latter being the critical index for Cesáro summability of Fourier--Laplace series on S n-1. The main purpose of this paper is to extend known results from the unit circle S 1to the general sphere S n-1 with n≥3. We prove six theorems. To prove Theorems 1-3, our machinery is based on the equiconvergent operator E δ N (f) of the Cesáro means σδ N (f) on S n-1 introduced by Wang Kunyang for δ>-1. We prove in Theorem 6 that E δ N (f) is also equiconvergent with σδ N (f) for δ>0 in the case of strong approximation. To prove Theorems 4 and 5, we rely on known equivalence relations between K-functionals and moduli of continuity. 相似文献
68.
We prove that the maximal Riesz operator $\sigma^{\alpha,\gamma}_*$ is of strong type from $L^1(\R) \cap H^p$ $ (\R)$ to $L^p (\R)$ for $\alpha, \gamma>0$ and $1/(1+\alpha) < p \le 1$, it is of weak type for $\alpha,\gamma>0$ and $1/(1+\alpha) = p$, and these results are best possible. The proofs are based on sharp estimates of the derivatives of the Riesz kernel. We characterize the real Hardy space $H^p(\R)$ in terms of $\sigma^{\alpha,1}_*$ for $1/(1+ \alpha) < p \le 1$, and draw consequences for real Hardy spaces on $\R^2$, as well. For example, an integrable function $f$ belongs to $H^1(\R)$ if and only if the maximal Fej\er operator $\sigma^{1,1}_*$ applied to $f$ belongs to $L^1(\R)$. We also establish analogous results for real Hardy spaces on $\T$ and $\T^2$. 相似文献
69.
Ferenc Móricz 《Analysis Mathematica》2004,30(2):123-136
A theorem of Fejér states that if a periodic function F is of bounded variation on the closed interval [0, 2], then the nth partial sum of its formally differentiated Fourier series divided by n converges to -1 [F(x+0) - F(x-0)] at each point x. The generalization of this theorem for Fourier-Stieltjes series of nonperiodic functions of bounded variation is also known. These theorems can be interpreted in such a way that the terms of the Fourier-Stieltjes (or Fourier) series of F determine the atoms of the finite Borel measure on the torus T:= [0, 2) induced by an appropriate extension of F (or by F itself in the periodic case). The aim of the present paper is to extend all of these results to the Cesàro as well as Abel-Poisson means of Fourier-Stieltjes (or Fourier) series of a nonperiodic (or periodic) function F of bounded variation. At the end, we sketch a possible extension of these results to linear means defined by more general kernels. 相似文献
70.
Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2003,286(1):340-350
Let be a double sequence of real or complex numbers, and set