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Autor:
Karagulyan, G. A.1 (AUTHOR) g.karagulyan@gmail.com, Karagulyan, V. G.2 (AUTHOR)
Publikováno v:
Mathematical Notes. Dec2023, Vol. 114 Issue 5/6, p1225-1232. 8p.
Publikováno v:
J. Math. Anal. Appl. 421 (2015), no. 1, 206-214
Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems established by Rodin in 1990. We prove, that if the growth of a function $\Phi(t):[0,\infty)\to[0,\infty)$ is bigger than the exponent, then the str
Externí odkaz:
http://arxiv.org/abs/1312.0855
Autor:
Karagulyan, G. A., Safaryan, M. H.
Publikováno v:
Hokkaido Mathematical Journal, 46(2017), no.1
In 1927 Littlewood constructed an example of bounded holomorphic function on the unit disk, which diverges almost everywhere along rotated copies of any given curve in the unit disk ending tangentially to the boundary. This theorem was the complement
Externí odkaz:
http://arxiv.org/abs/1311.3750
Autor:
Karagulyan, G. A., Safaryan, M. H.
Publikováno v:
The Journal of Geometric Analysis, 25(2015), no 3, p 1459-1475
We define $\lambda(r)$-convergence, which is a generalization of nontangential convergence in the unit disc. We prove Fatou-type theorems on almost everywhere nontangential convergence of Poisson-Stiltjes integrals for general kernels $\{\varphi_r\}$
Externí odkaz:
http://arxiv.org/abs/1310.8061
Publikováno v:
Constr. Approx. 40 (2014), no. 1, 105-120
It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series.
Externí odkaz:
http://arxiv.org/abs/1303.0364
Autor:
Karagulyan, G. A.
Publikováno v:
Proc. Amer. Math. Soc., 139(2011), No 7,2543-2552
Let $\mu_n$ be a sequence of discrete measures on the unit $\ZT=\ZR/\ZZ$ with $\mu_n(0)=0$, and $\mu_n((-\delta,\delta))\to 1$, as $n\to\infty$. We prove that the sequence of convolution operators $(f\ast\mu_n)(x)$ is strong sweeping out, i.e. there
Externí odkaz:
http://arxiv.org/abs/1210.1956
Autor:
Karagulyan, G. A.
We consider sequences of linear operators $U_nf(x)$ with localization property. It is proved that for any set $E$ of measure zero there exists a set $G$ for which $U_n\ZI_G(x)$ diverges at each point $x\in E$. This result is a generalization of analo
Externí odkaz:
http://arxiv.org/abs/0912.1453
Autor:
Karagulyan, G. A.
In this paper we investigate problems on almost everywhere convergence of subsequences of Riemann sums \md0 R_nf(x)=\frac{1}{n}\sum_{k=0}^{n-1}f\bigg(x+\frac{k}{n}\bigg),\quad x\in \ZT. \emd We establish a relevant connection between Riemann and ordi
Externí odkaz:
http://arxiv.org/abs/0803.4392
Autor:
Karagulyan, G. A.
We show that for any infinite set of unit vectors $U$ in $\ZR^2$ the maximal operator defined by $$ H_Uf(x)=\sup_{u\in U}\bigg|\pv\int_{-\infty}^\infty \frac{f(x-tu)}{t}dt\bigg|,\quad x\in \ZR^2, $$ is not bounded in $L^2(\ZR^2)$.
Comment: Publi
Comment: Publi
Externí odkaz:
http://arxiv.org/abs/math/0602524